REESE  LIBRARY 

OF  THK 

UNIVERSITY  OF  CALIFORNIA. 

Deceived  ,  igo     . 

Accession  No.       83054  •   Class  No. 


HARPER'S  SCIENTIFIC  MEMOIRS 

EDITED  BY 

J.  S.  AMES,  PH.D. 

PKOKKSSOK   OK   PHYSICS    IN    JOHNS   HOPKINS    UNIVERSITY 


V. 
THE    LAWS    OF    GASES 


THE    LAWS    OF    GASES 


MEMOIRS  BY  ROBERT  BOYLE  AND 
E.  H.  AMAGAT 


TRANSLATED  AND  EDITED  BY 

CARL    BARUS 

PROFESSOR   OF   PHYSICS   IN   BROWN   UNIVERSITY 
I 


NEW   YORK  AND  LONDON 

HARPER    &    BROTHERS    PUBLISHERS 
1899 


HARPER'S    SCIENTIFIC   MEMOIRS, 

EDITED    BY 

J.    S.  AMKS,  PH.D., 

PKOFKSSOR    OF    PHYSICS    IN    JOHNS    HOPKINS  UNIVKK8ITY. 


SOW  READY: 

THE  FREE  EXPANSION  OF  GASES.  Memoirs 
by  Gay-Lussac,  Joule,  and  Jonle  and  Thomson. 
Editor,  Prof.  J.  S.  AMKS,  Ph.D.,  .Johns  Hopkins 
University.  75  cents. 

PRISMATIC  AND  DIFFRACTION  SPECTRA. 
Memoirs  by  Joseph  von  Fraunhofer.  Editor,  Prof. 
J.  S.  AMKS,  Ph.D.,  Johns  Hopkins  University. 
GO  cents. 

RONTGEN  RAYS.  Memoirs  by  Rontgen,  Stokes, 
and  J.  J.  Thomson.  Editor,  Prof.  GKOKGK  F. 
BAEKKR,  University  of  Pennsylvania.  GO  cents. 

THE  MODERN  THEORY  OF  SOLUTION.  Me- 
moirs by  Pfeffer,  Van't^Hoff,  Arrhenius,  and  Raoult. 
Editor,  Dr.  H.  C.  JONKS,  Johns  Hopkins  University. 
$100. 

THE  LAWS  OF  GASES.  Memoirs  by  Boyle  and 
Amagat.  Editor,  Prof.  C  A  ur,  BAUDS,  Brown  University. 

fX  PREPARATION: 

THE  SECOND  LAW  OF  THERMODYNAMICS. 
Memoirs  by  Caruot,  Clausius,  and  Thomson.  Editor, 
Prof.  W.  F.  MAGIK,  Princeton  University. 

THE  FUNDAMENTAL  LAWS  OF  ELECTRO- 
LYTIC CONDUCTION.  Memoirs  by  Faraday, 
Hittorf,  and  Kohlransch.  Editor,  Dr.  H.  M.  GOOD- 
WIN, Massachusetts  Institute  of  Technology. 

THE  EFFECTS  OF  A  MAGNETIC  FIELD  ON 
RADIATION.  Memoirs  by  Faraday,  Kerr,  and 
Zeeinan.  Editor,  Dr.  E.  P.  LKWIS,  University  of 
California. 

WAVE-THEORY  OF  LIGHT.  Memoirs  by  Hnygens, 
Young,  and  Fresnel.  Editor,  Prof.  HKNKY  CHEW, 
Northwestern  University. 

NEWTON'S  LAW  OF  GRAVITATION.  Editor, 
Prof.  A.  S.  MACKKNZIK,  Bryn  Mawr  College. 

NEW    YORK    AND    LONDON: 

HARPER  &  BROTHERS,  PUBLISHERS. 


Copyright,  1899,  by  HAKPEK  &  BKOTUKKS. 


All  rights  reserved. 


PKEFACE 


OF  course  anybody  may  read  the  famous  Memoirs  of  Ama- 
gat  in  the  original;  but  everybody  cannot  so  easily  get  these 
papers  permanently  into  his  possession.  I  believe,  therefore, 
with  the  present  translations  to  have  scored  a  point  in  the  in- 
terest of  accessibility,  and  thus  to  have  materially  contributed 
to  the  advancement  of  science. 

C.  B. 

BROWN  UNIVERSITY,  Providence,  R.  I., 
March,  1899. 


83054 


GENERAL   CONTENTS 


HAGK 

Preface v 

A  Defence  of  the  Doctrine  Touching  the  Spring  and  Weight  of  the 

Air,  proposed  by  Mr.  R.  BOYLE  in  his  new  Physico-Mechan- 

ical  Experiments,  against  the  Objections  of  Franciscus  Linus.  3 

Biographical  Sketch  of  Boyle 10 

On  the  Compressibility  of  Gases  at  High  Pressures.  By  E.  H.  Amagat  13 
On  the  Elasticity  and  the  Thermal  Expansion  of  Fluids  Throughout 

an  Interval  Terminating  in  Very  High  Pressures.     By  E.  H. 

Amagat 53 

Biographical  Sketch  of  Amagat 107 

Bibliography 108 


A  DEFENCE  OF 

THE  DOCTEINE  TOUCHING  THE  SPEING 
AND  WEIGHT  OF  THE  AIE 

Proposed  by  Mr.  R.  BOYLE  in  his  New  Physico- Mechanical  Experiments,. 

against  the  Objections  of  FHANCISCUS  LINUS,  wherewith  the 

Objector's  Funicular  Hypothesis  is  also  Examined 

London,  1662 


A  DEFENCE  OF 

THE  DOCTRINE  TOUCHING  THE  SPRING 
AND  WEIGHT  OF  THE  AIR* 

BY   ROBERT   BOYLE 


PART  II.,  CHAPTER  V. 

TWO   NEW   EXPERIMENTS   TOUCHING   THE   MEASURE   OP  THE   FORCE  OP  THE 
SPRING   OF   AIR   COMPRESSED   AND   DILATED 

We  took  then  a  long  glass-tube,  which,  by  a  dexterous  hand 
and  the  help  of  a  lamp,  was  in  such  a  manner  crooked  at  the 
bottom,  that  the  part  turned  up  was  almost  parallel  to  .the  rest 
of  the  tube,  and  the  orifice  of  this  shorter  leg  of  the  siphon  (if 
I  may  so  call  the  whole  instrument)  being  hermetically  sealed, 
the  length  of  it  was  divided  into  inches  (each  of  which  was 
subdivided  into  eight  parts)  by  a  streight  list  of  paper,  which 
containing  those  divisions,  was  carefully  pasted  all  along  it. 
Then  putting  in  as  much  quicksilver  as  served  to  fill  the  arch 
or  bended  part  of  the  siphon,  that  the  mercury  standing  in  a 
level  might  reach  in  the  one  leg  to  the  bottom  of  the  divided 
paper,  and  just  to  the  same  height  or  horizontal  line  in  the 
other  ;  we  took  care,  by  frequently  inclining  the  tube,  so  that 
the  air  might  freely  pass  from  one  leg  into  the  other  by  the 
sides  of  the  mercury  (we  took,  I  say,  care)  that  the  air  at  last 
included  in  the  shorter  cylinder  should  be  of  the  same  laxity 
with  the  rest  of  the  air  about  it.  This  done,  we  began  to  pour 
quicksilver  into  the  longer  leg  of  the  siphon,  which  by  its  weight 
pressing  up  that  in  the  shorter  leg,  did  by  degrees  streighten 

*  Selected  from  Boyle's  New  Physico  -  Mechanical  Experiments,  Lon- 
don, 1662. 

3 


MEMOIRS,  ON 

the  included  air  :  and  continuing  this  pouring  in  of  quicksilver 
till  the  air  in  the  shorter  leg  was  by  condensation  reduced  to 
take  up  but  half  the  space  it  possessed  (I  say,  possessed,  not 
filled)  before  ;  we  cast  our  eyes  upon  the  longer  leg  of  the  glass, 
on  which  was  likewise  pasted  a  list  of  paper  carefully  divided 
into  inches  and  parts,  and  we  observed,  not  without  delight 
and  satisfaction,  that  the  quicksilver  in  that  longer  part  of  the 
tube  was  29  inches  higher  than  the  other.  Now  that  this 
observation  does  both  very  well  agree  with  and  confirm  our 
hypothesis,  will  be  easily  discerned  by  him  that  takes  notice 
what  we  teach  ;  and  Monsieur  Paschal  and  our  English  friend's 
experiments  prove,  that  the  greater  the  weight  is  that  leans 
upon  the  air,  the  more  forcible  is  its  endeavour  of  dilatation, 
and  consequently  its  power  of  resistance  (as  other  springs  are 
stronger  when  bent  by  greater  weights).  For  this  being  con- 
sidered, it  will  appear  to  agree  rarely-well  with  the  hypothesis, 
that  as  according  to  it  the  air  in  that  degree  of  density  and 
correspondent  measure  of  resistance,  to  which  the  weight  of 
the  incumbent  atmosphere  had  brought  it,  was  able  to  counter- 
balance and  resist  the  pressure  of  a  mercurial  cylinder  of  about 
29  inches,  as  we  are  taught  by  the  Torricellian  experiment ; 
so  here  the  same  air  being  brought  to  a  degree  of  density  about 
twice  as  great  as  that  it  had  before,  obtains  a  spring  twice  as 
strong  as  formerly.  As  may  appear  by  its  being  able  to  sustain 
or  resist  a  cylinder  of  29  inches  in  the  longer  tube,  together 
with  the  weight  of  the  atmospherical  cylinder,  that  leaned  upon 
those  29  inches  of  mercury;  and,  as  we  just  now  inferred  from 
the  Torricellian  experiment,  was  equivalent  to  them. 

We  were  hindered  from  prosecuting  the  trial  at  that  time 
by  the  casual  breaking  of  the  tube.  But  because  an  accurate 
experiment  of  this  nature  would  be  of  great  importance  to  the 
doctrine  of  the  spring  of  the  air,  and  has  not  yet  been  made 
(that  I  know)  by  any  man  ;  and  because  also  it  is  more  uneasy 
to  be  made  than  one  would  think,  in  regard  of  the  difficulty  as 
well  of  procuring  crooked  tubes  fit  for  the  purpose,  as  of  making 
a  just  estimate  of  the  true  place  of  the  protuberant  mercury's 
surface ;  I  suppose  it  will  not  be  unwelcome  to  the  reader  to  be 
informed,  that  after  some  other  trials,  one  of  which  we  made 
in  a  tube  whose  longer  leg  was  perpendicular,  and  the  other, 
that  contained  the  air,  parallel  to  the  horizon,  we  at  last  pro- 
cured a  tube  of  the  figure  expressed  in  the  scheme;  which 

4 


OF   THE 

UNIVERSl' 


THE    LA 


OF  .GASES 


tube,  though  of  a  pretty  bigness,  was  so  long,  that  the  cylinder, 
whereof  the  shorter  leg  of  it  consisted,  admitted  a  list  of  paper, 
which  had  before  been  divided  into  12  inches  and  their  quarters, 
and  the  longer  leg  admitted  another  list  of  paper  of  divers  feet 
in  length,  and  divided  after  the  same  manner.  Then  quicksilver 
being  poured  in  to  fill  up  the  bended  part  of  the  glass,  that  the 
surface  of  it  in  either  leg  might  rest  in  the  same  horizontal  line, 
as  we  lately  taught,  there  was  more  and  more  quicksilver  poured 
into  the  longer  tube ;  and  notice  being  watchfully  taken  how 
far  the  mercury  was  risen  in  that  longer  tube,  when  it  appeared 
to  have  ascended  to  any  of  the  divisions  in  the  shorter  tube, 
the  several  observations  that  were  thus  successively  made,  and 
as  they  were  made  set  down,  afforded  us  the  ensuing  table  : 

A   TABLE   OF   THE   CONDENSATION"   OP   THE   AIR 


A 

A 

B 

C 

D 

E 

48 

12 

00 

29* 

29* 

A  A.  The  number  of  equal 

46 
44 

11* 

11. 

01* 

02f| 

30^ 

33^ 

spaces   in   the    shorter 
leg,  that  contained  the 
same   parcel  of  air  di- 

42 

m 

04y^- 

33* 

33J 

versely  extended. 

40 

10 

06A 

35* 

35 

38 

91. 

07H 

37 

36^f 

B.  The  height  of  the  mer- 

36 
34 
32 

9 

8* 

8 

ipA 

ISA 

02 
<D 

39I! 

38| 
41* 
43# 

curial  cylinder  in  the 
longer  leg,  that  com- 
pressed   the    air    into 
those  dimensions. 

30 

7£ 

17« 

•a 

47TV 

46| 

28 

7 

21  3 

s 

50* 

50 

C.  The  height  of  the  mer- 

26 
24 
23 

6* 

6    . 

25A 

89ft 

3*A 

o 

54* 

58H 

58f 
60H 

curial     cylinder,    that 
counterbalanced    the 
pressure  of  the  atmos- 
phere. 

22 

5j 

34^-f- 

0) 

64* 

631T 

21 

37^f 

rd 
•n 

67* 

D.  The  aggregate  of  the 

20 

5 

41* 

70 

two  last  columns,  j?and 

19 

1  6 

45 

74* 

(7,  exhibiting  the  press- 
ure  sustained    by    the 

18 

4 

48yf 

77-J-f 

77f9 

included  air. 

17 

4J 

53H 

82i| 

82T\ 

16 

4 

58-fr 

87f| 

87| 

E.  What    that    pressure 

15 
14 

3f 

63H 

93TV 
100TV 

93* 

99f 

should  be  according  to 
the     hypothesis,     that 
supposes  the  pressures 

13 

3£ 

78^|- 

107  ff 

1°7* 

and  expansions  to  be  in 

12 

3 

88* 

117* 

116f 

reciprocal  proportion. 

5 

MEMOIRS    ON 

For  the  better  understanding  of  this  experiment,  it  may  not 
be  amiss  to  take  notice  of  the  following  particulars  : 

1.  That  the  tube  being  so  tall  that  we  could  not  conveniently 
make  use  of  it  in  a  chamber,  we  were  fain  to  use  it  on  a  pair 
of  stairs,  which  were  yet  very  lightsome,  the  tube  being  for 
preservation's  sake  by  strings  so  suspended  that  it  did  scarce 
touch  the  box  presently  to  be  mentioned. 

2.  The  lower  and  crooked  part  of  the  pipe  was  placed  in  a 
square  wooden  box,  of  a  good  largeness  and  depth,  to  prevent 
the  loss  of  the  quicksilver,  that  might  fall  aside  in  the  transfu-' 
sion  from  the  vessel  into  the  pipe,  and  to  receive  the  whole 
quicksilver  in  case  the  tube  should  break. 

3.  That  we  were  two  to  make  the  observation  together,  the 
one  to  take  notice  at  the  bottom,  how  the  quicksilver  rose  in 
the  shorter  cylinder,  and  the  other  to  pour  in  at  the  top  of  the 
longer ;  it  being  very  hard  and  troublesome  for  one  man  alone 
to  do  both  accurately. 

4.  That  the  quicksilver   was  poured   in  but  by  little  and 
little,  according  to  the  direction  of  him  that  observed  below  : 
it  being  far  easier  to  pour  in  more  than  to  take  out  any,  in  case 
too  much  at  once  had  been  poured  in. 

5.  That  at  the  beginning  of  the  operation,  that  we  might  the 
more  truly  discern  where  the  quicksilver  rested  from  time  to 
time,  we  made  use  of  a  small  looking-glass  held  in  a  conven- 
ient posture  to  reflect  to  the  eye  what  we  desired  to  discern. 

6.  That  when  the  air  was  so  comprest  as  to  be  crouded 
into  less  than  a  quarter  of  the  space  it  possessed  before,  we 
tried  whether  the  cold  of  a  linen  cloth  dipped  in  water  would 
then  condense  it.     And  it  sometimes  seemed  a  little  to  shrink, 
but  not  so  manifestly  that  we  dare  build  anything  upon  it. 
We  then  tried  likewise,  whether  heat  would,  notwithstanding 
so  forcible  a  compressure,  dilate  it ;  and  approaching  the  flame 
of  a  candle  to  that  part  where  the  air  was  pent  up,  the  heat 
had  a  more  sensible  operation  than  the  cold  had  before  ;   so 
that  we  scarce  doubted,  but  that  the  expansion  of  the  air  would, 
notwithstanding  the  weight  that  comprest  it,  have  been  made 
conspicuous,  if  the  fear  of  unseasonably  breaking  the  glass  had 
not  kept  us  from  increasing  the  heat. 

Now  although  we  deny  not,  but  that  in  our  table  some  par- 
ticulars do  not  so  exactly  answer  to  what  our  formerly  men- 
tioned hypothesis  might  perchance  invite  the  reader  to  expect ; 

6 


THE    LAWS    OF    GASES 

yet  the  variations  are  not  so  considerable,  but  that  they  may 
probably  enough  be  ascribed  to  some  such  want  of  exactness 
us  in  such  nice  experiments  is  scarce  avoidable.  But  for  all 
that,  till  further  trial  hath  more  clearly  informed  me,  I  shall 
not  venture  to  determine  whether  or  no  the  intimated  theory 
will  hold  universally  and  precisely,  either  in  condensation  of 
air  or  rarefaction  :  all  that  I  shall  now  urge  being,  that  however 
the  trial  already  made  sufficiently  proves  the  main  thing,  for 
which  I  here  allege  it ;  since  by  it,  it  is  evident,  that  as  com-\  ' 
mon  air,  when  reduced  to  half  its  wonted  extent,  obtained  near 
about  twice  as  forcible  a  spring  as  it  had  before  ;  so  this  thus) 
comprest  air  being  further  thrust  into  half  this  narrow  room, 
obtained  thereby  a  spring  about  as  strong  again  as  that  it  last 
had,  and  consequently  four  times  as  strong  as  that  of  the  com- 
mon air.  And  there  is  no  cause  to  doubt,  that  if  we  had  been 
here  furnished  with  a  greater  quantity  of  quicksilver  and  a 
very  strong  tube,  we  might,  by  a  further  compression  of  the 
included  air,  have  made  it  counterbalance  the  pressure  of  a  far 
taller  and  heavier  cylinder  of  mercury.  For  no  man  perhaps 
yet  knows  how  near  to  an  infinite  compression  the  air  may  be 
capable  of,  if  the  compressing  force  be  competently  increased. 

And  to  let  you  see,  that  we  did  not  (as  a  little  above)  incon- 
siderately mention  the  weight  of  the  incumbent  atmospherical 
cylinder  as  a  part  of  the  weight  resisted  by  the  imprisoned  air, 
we  will  here  annex,  that  we  took  care;  when  the  mercurial  cyl- 
inder in  the  longer  leg  of  the  pipe  was  about  an  hundred  inches 
high,  to  cause  one  to  suck  at  the  open  orifice ;  whereupon  (as 
we  expected)  the  mercury  in  the  tube  did  notably  ascend.  .  .  . 
And  therefore  we  shall  render  this  reason  of  it  that  the  press- 
ure of  the  incumbent  air  being  in  part  taken  off  by  its  ex- 
panding itself  into  the  sucker's  dilated  chest,  the  imprisoned 
air  was  thereby  enabled  to  dilate  itself  manifestly,  and  repel 
the  mercury,  that  comprest  it,  till  there  "was  an  equality  of 
force  betwixt  the  strong  spring  of  that  comprest  air  on  the 
one  part,  and  the  tall  mercurial  cylinder,  together  with  the 
contiguous  dilated  air,  on  the  other  part. 

Now,  if  to  what  we  have  thus  delivered  concerning  the  com- 
pression of  the  air,  we  add  some  observations  concerning  its 
spontaneous  expansion,  it  will  the  better  appear,  how  much 
the  phenomena  of  these  mercurial  experiments  depend  upon 

7 


MEMOIRS    ON 

the  differing  measures  of  strength  to  be  met  with  in  the  air's 
spring,  according  to  its  various  degrees  of  compression  and 
laxity. 


A  TABLE  OF  THE  RAREFACTION  OF  THE  AIR 


A 

B 

0 

D 

E 

A.  The  number  of  equal  spaces  at 

1 

00{f 

29| 

29} 

the   top   of   the   tube,  that  con- 
tained the  same  parcel  of  air. 

2 

io| 

lof 

19| 

19f 

3 

204 

9| 

9.^5. 

B.  The  height  of  the  mercurial  cyl- 

4 

224 

CO 

® 

H 

w 

inder,    that    together    with     the 

5 

24-J 

1 

5! 

5^f 

spring  of  the  included   air  coun- 

6 

24} 

4f^ 

terbalanced  the  pressure  of  the 

7 

OS 

41 

41 

atmosphere. 

8 

26£ 

B 

si 

344 

9 

264 

2 

3| 

3^| 

C.  The  pressure  of  the  atmosphere. 

10 

264 

tj 

3* 

w 

12 

27-J- 

.j-j 

2| 

2» 

14 

274 

g 

2-| 

2-| 

D.  The  complement  of  B  to  C,  ex- 

16 

274 

-§ 

2-J 

l|f 

hibiting   the    pressure   sustained 
by  the  included  air. 

18 
20 

n 

p 
dp 

4 

24 

284 

it 

ill 

K.  What  that  pressure  should  be, 

28 

284 

H 

1TV 

according  to  the  hypothesis. 

32 

284 

if 

Olil 

To  make  the  experiment  of  the  debilitated  force  of  expanded 
air  the  plainer,  it  will  not  be  amiss  to  note  some  particulars, 
especially  touching  the  manner  of  making  the  trial  ;  which 
(for  the  reasons  lately  mentioned)  we  have  made  on  a  light- 
some pair  of  stairs,  and  with  a  box  also  lined  with  paper  to 
receive  the  mercury  that  might  be  spilt.  And  in  regard  it 
would  require  a  vast  and  in  few  places  procurable  quantity 
of  quicksilver,  to  imploy  vessels  of  such  kind  as  are  ordinary 
in  the  Torricellian  experiment,  we  made  use  of  a  glass-tube  of 
about  six  feet  long ;  for  that  being  hermetically  sealed  at  one 
end,  served  our  turn  as  well  as  if  we  could  have  made  the  ex- 
periment in  a  tub  or  pond  of  seventy  inches  deep. 

Secondly,  We  also  provided  a  slender  glass-pipe  of  about  the 

8 


THE    LAWS    OF    GASES 

bigness  of  a  swan's  quill,  and  open  at  both  ends  ;  all  along 
which  was  pasted  a  narrow  list  of  paper,  divided  into  inches 
and  half  quarters. 

Thirdly,  This  slender  pipe  being  thrust  down  into  the  greater 
tube  almost  filled  with  quicksilver,  the  glass  helped  to  make  it 
swell  to  the  top  of  the  tube  ;  and  the  quicksilver  getting  in  at 
the  lower  orifice  of  the  pipe,  filled  it  up  until  the  mercury  in- 
cluded in  that  was  near  about  a  level  with  the  surface  of  the 
surrounding  mercury  in  the  tube. 

Fourthly,  There  being,  as  near  as  we  could  guess,  little  more 
than  an  inch  of  the  slender  pipe  left  above  the  surface  of  the 
restagnant  mercury,  and  consequently  unfilled  therewith,  the 
prominent  orifice  was  carefully  closed  with  sealing  wax  melted; 
after  which  the  pipe  was  let  alone  for  a  while,  that  the  air, 
dilated  a  little  by  the  heat  of  the  wax,  might,  upon  refrigera- 
tion, be  reduced  to  its  wonted  density.  And  then  we  observed 
by  the  help  of  the  above  mentioned  list  of  paper,  whether  we 
had  not  included  somewhat  more  or  somewhat  less  than  an 
inch  of  air  ;  and  in  either  case  we  were  fain  to  rectify  the  error 
by  a  small  hole  made  (with  a  heated  pin)  in  the  wax,  and  after- 
wards closed  up  again. 

Fifthly,  Having  thus  included  a  just  inch  of  air,  we  lifted  up 
the  slender  pipe  by  degrees,  till  the  air  was  dilated  to  an  inch, 
an  inch  and  an  half,  two  inches,  &c.,  and  observed  in  inches 
and  eighths  the  length  of  the  mercurial  cylinder,  which  at  each 
degree  of  the  air's  expansion  was  impelled  above  the  surface  of 
the  restagnant  mercury  in  the  tube. 

Sixthly,  The  observations  being  ended,  we  presently  made 
the  Torricellian  experiment  with  the  above-mentioned  great 
tube  of  six  feet  long,  that  we  might  know  the  height  of  the 
mercurial  cylinder,  for  that  particular  day  and  hour  ;  which 
height  we  found,  to  be  29|  inches. 

Seventhly,  Our  observations  made  after  this  manner  fur- 
nished us  with  the  preceding  table,  in  which  there  would  not 
probably  have  been  found  the  difference  here  set  down  betwixt 
tho  force  of  the  air,  when  expanded  to  double  its  former  dimen- 
sions, and  what  that  force  should  have  been  precisely  according 
to  the  theory,  but  that  the  included  inch  of  air  received  some 
little  accession  during  the  trial  ;  which  this  newly  mentioned 
difference  making  us  suspect,  we  found  byreplunging  the  pipe 
into  the  quicksilver,  that  the  included  air  had  gained  about 

9 


OF    THK 

UNIVERSITY 


MEMOIRS    ON    THE    LAWS    OF    GASES 

half  an  eighth,  which  we  guessed  to  have  come  from  some  little 
aerial  bubbles  in  the  quicksilver,  contained  in  the  pipe  (so  easy 
is  it  in  such  nice  experiments  to  miss  of  exactness). 


The  Honorable  ROBERT  BOYLE  was  born  in  Ireland,  County 
Cork,  January  25,  1626,  and  died  in  London,  December  30, 
1691.  He  made  his  home  in  Oxford  from  1654  to  1668,  when 
he  moved  to  London.  It  was  while  living  at  Oxford  that  he 
invented  the  air-pump,  which  was  perfected  for  him  in  1658 
or  1659  by  his  assistant  in  chemistry,  Robert  Hooke,  who  was 
afterwards  so  famous.  In  1663,  at  the  incorporation  of  the 
Royal  Society  by  King  Charles  II.,  Boyle  wao  appointed  by  the 
charter  one  of  the  council,  as  he  had  been  one  of  the  persons 
to  whom  the  society  owed  its  origin.  He  was  elected  president 
of  the  society  in  November,  1680;  but  on  account  of  "the 
obligation  to  take  the  test  and  oaths,"  he  felt  obliged  to  de- 
cline the  honor. 

It  was  in  1660  that  he  published  his  first  experiments,  On 
the  Spiring  of  the  Air,  and  in  1662  that  he  announced  the  law 
of  gases  that  bears  his  name.  These  experiments  were  repeat- 
ed later,  by  Mariotte  in  France,  and  were  published  by  him  in 
1676. 

Boyle  published  a  great  many  papers  in  the  Philosophical 
Transactions,  and  was  actively  engaged  in  scientific  work  up  to 
the  last  years  of  his  life.  It  is  worthy  of  note  that  nearly  all 
the  common  lecture -experiments  in  hydrostatics  and  pneu- 
matics are  due  to  Boyle. 


ON  THE  OOMPEESSIBILITY  OF  GASES  AT 
HIGH  PRESSURES 

BY 

E.  H.  AMAGAT 

(Annales  de  Chimie  et  de  Physique,  5e  serie,  t.  xxil,  pp.  353-398,  1881) 


CONTENTS 

PAGE 

Introductory 13 

Description  of  the  Apparatus 15 

Method  of  Experimentation 19 

Method  of  Calculation , 20 

Numerical  Results 23 

Examination  and  Discussion  of  the  Results 26 

Dilatation  of  Gases  at  High  Pressures 36 

Covolume — Atomic  Volume , .  39 


ON  THE  COMPRESSIBILITY  OF  GASES  AT 
HIGH  PRESSURES 

BY  E.  H.  AMAGAT 


INTRODUCTORY 

IN  1869,  when  I  communicated  the  results  of  my  first  experi- 
ments relative  to  the  effect  of  temperature  on  the  compressi- 
bility of  a  gas,  no  direct  experiments  had  been  made  on  this 
subject.  It  was  customary  merely  to  quote  Regnault's  infer- 
ences touching  the  behavior  of  carbon  dioxide  at  100°  C.  At 
this  temperature,  since  the  density  of  the  gas  is  sensibly  in- 
dependent of  pressure  for  pressures  in  the  neighborhood  of  1 
atmosphere,  one  may  conclude  that  under  the  conditions  stated 
the  gas  appreciably  follows  Mariotte's  law.  Nevertheless,  the 
inference  of  Regnault  is  in  need  of  slight  modification.  My 
results  proved  that  at  100°,  carbon  dioxide,  although  diverging 
less  from  the  law  than  at  ordinary  temperatures,  is  quite  sen- 
sibly divergent;  and  M.  Blaserna  showid^  a  short  time  after- 
wards that  the  discrepancy  arose  out  of  an  error  which  slipped 
into  the  numerical  calculations  of  Eegnault.  Indeed,  M.  Bla- 
serna arrived  at  an  analogous  conclusion  himself  in  a  purely  theo- 
retical paper  published  in  the  Annales  de  Chimie  et  de  Physique 
in  1865  (t.  v.). 

In  1872  I  made  a  complete  publication  f  of  my  researches  on 
this  subject,  having  studied  ammonia  as  far  as  100°,  sulphur 
dioxide  and  carbon  dioxide  as  far  as  250°,  and  air  and  hydrogen 
up  to  320°. 

I  then  believed  that  at  temperatures  sufficiently  low  all  gases 

*  Oomptes  Eendus  des  /Seances  de  I'Academie  des  Sciences,  t.  xlix.,  1869. 
t  Annales  de  Chimie  et  de  Physique,  t.  xxix.,  1873. 

13 


MEMOIRS    ON 

behave  like  carbon  dioxide ;  but  that  as  temperature  increases 
gases  begin  more  and  more  to  follow  the  law  of  Mariotte,  finally 
to  depart  from  it  indefinitely  in  a  contrary  sense  as  does  hy- 
drogen at  ordinary  atmospheric  temperatures.  It  follows  nat- 
urally that  nitrogen,  which,  as  I  showed,  obeys  Mariotte's  law 
as  far  as  100°  and  between  1  and  2  atmospheres,  presents  a  neg- 
ative discrepancy  below  that  temperature  ;  and  that  hydrogen 
more  and  more  highly  heated  continues  to  present  an  in- 
variably negative  divergence  of  increasing  value.  Experiment, 
however,  has  shown  me  that  at  200°  the  divergence  of  air  al- 
ways sensibly  zero  does  not  from  the  shape  of  the  curves  tend 
to  become  negative,  and  that  even  for  the  case  of  hydrogen 
the  discrepancy  tends  rather  to  vanish  than  to  increase  in  the 
negative  direction  or  to  remain  negative.  Naturally  I  then  in- 
ferred that  the  effect  of  temperature  was  an  approach  of  both 
gases  towards  the  law,  the  compressibility  of  the  first  being  di- 
minished and  that  of  the  other  increased. 

It  will  be  seen  in  the  course  of  the  present  paper  that  this 
conclusion  is  correct  relative  to  hydrogen,  but  that  for  air  the 
interpretation  of  the  results  will  have  to  be  changed.  It  will 
also  be  seen  that  it  must  be  impossible  to  arrive  at  a  knowledge 
of  the  general  laws  for  gases  as  long  as  the  investigations  are 
limited  to  an  interval  of  pressure  within  which  the  trend  of 
the  discrepancies  hardly  even  begins  to  appear  ;  that  these  laws 
will  not  be  manifest  in  their  entirety  until  the  experiments  are 
pushed  forward  throughout  several  hundred  atmospheres;  that, 
finally,  all  that  has  hitherto  been  known  about  the  compressi- 
bility of  gases  would  not  have  enabled  any  one  to  even  suspect 
the  laws  in  their  true  characters,  such  as  I  shall  establish  them 
below. 

I  shall  not  enter  into  any  details  as  to  the  formulas  by  aid 
of  which  different  physicists  have  sought  to  express  the  effect 
of  temperature  on  the  compressibility  of  gases.  These  for- 
mulas, as  a  rule  purely  empyric,  are  not  applicable  except  within 
very  narrow  pressure-limits;  moreover,  I  shall  have  occasion  to 
speak  of  them  in  the  near  future  in  a  paper  referring  specially 
to  low  pressures. 

During  the  course  of  my  experiments  I  was  able  to  show  that, 
even  after  making  allowance  for  atomic  volume,  the  shortcom- 
ings of  Mariotte'*s  law  cannot  be  explained  fully  by  postulat- 
ing an  internal  pressure  tending  to  move  the  molecules  nearer 

14 


THE    LAWS    OF    GASES 

together,  because  this  pressure  would  be  different  for  the  same 
mean  distance  of  the  molecules  at  different  temperatures.  I 
shall  return  to  this  point  below,  and  then  complete  the  demon- 
stration by  comparing  the  results  at  which  I  have  arrived  with 
those  predicted  by  the  theory  of  M.  Him. 

Eecently  M.  Winkelmann  has  published  the  results  of  experi- 
ments made  with  ethylene  between  0°  and  100°  and  between 
1  and  2  atmospheres.  He  finds,  corroboratively,  that  at  100° 
ethylene  obeys  the  law  of  Mariotte  more  nearly  than  at  0°  C. 
This  is  precisely  my  deduction  for  all  the  gases  treated  up  to 
100°,  250°,  and  320°. 

With  the  exception  of  these  experiments  and  those  described 
in  the  classical  memoir  of  Andrews  on  the  critical  point,  I 
believe  that  no  other  experimental  data  are  available,  barring 
the  results  which  I  adduced  in  the  memoir  summarizing  my 
experiments. 

As  to  laws  treating  of  the  manner  in  which  the  compressi- 
bility of  a  gas  is  modified  at  high  pressures  throughout  different 
temperatures,  they  are  quite  unknown.  It  was,  therefore,  with 
the  purpose  of  filling  this  important  gap  that  I  undertook  the 
researches  which  make  up  the  subject  of  the  present  memoir. 

I  have  studied  the  gases  nitrogen,  hydrogen,  marsh  gas, 
ethylene,  and  carbon  dioxide.  As  for  air,  and  particularly 
oxygen,  I  fear  that  at  the  higher  temperatures  the  action  of 
the  latter  gas  on  mercury  will  be  too  rapid  to  admit  of  the 
necessary  measurements,  and  this  in  greater  degree  as  the 
experiments  are  more  prolonged  under  the  conditions  of  high 
temperatures  stated. 

At  ordinary  temperatures,  on  the  other  hand,  the  experi- 
ments can  be  conducted  with  relatively  great  despatch.  A 
series  of  six  determinations  may  be  made  with  rigor  in  a 
quarter  of  an  hour,  and  then  all  oxidation  is  inappreciable. 
Hence,  in  my  first  research  I  was  able  to  study  these  two  gases 
(by  the  method  of  comparison)  without  being  annoyed  by  the 
difficulty  in  question.  It  is  my  object,  moreover,  to  make  a 
special  study  of  it  at  some  other  time. 


DESCRIPTION    OF    THE    APPARATUS 

The  apparatus  of  which  I  here  make  use  is  the  same  which 
has   already    served    me    in    the    determination    at    ordinary 

15 


MEMOIRS    ON 

temperatures  of  the  compressibility  of  the  gases  air,  oxygen, 
hydrogen,  carbon  dioxide,  marsh  gas,  and  ethylene,  in  com- 
parison with  nitrogen.  I  have  briefly  referred  to  it  in  my 
first  memoir  without  giving  a  full  description.  However,  as 
on  that  occasion  I  entered  with  considerable  detail  into  the 
construction  of  divers  parts  of  this  class  of  instruments,  I  am 
able  to  confine  myself  to  narrower  limits  here. 

Figure  1  shows  the  apparatus  drawn  to  a  scale  of  one-twelfth 
actual  size.  On  the  right  hand  is  the  nitrogen  manometer.* 
It  has  the  identical  dimensions  and  is  mounted  in  quite  the 
same  manner  as  the  one  on  the  machine  described  in  my  first 
memoir  on  the  subject.  In  this  case  it  was  used  to  measure 
the  compressibility  of  nitrogen  in  the  Verpilleux  mine  shaft. 
The  jacket  through  which  the  current  of  water  circulates  and 
the  enclosed  thermometer  are  attached  in  the  same  way.  The 
lid  or  flange  which  carries  the  whole  is  secured  by  four  bolts  to 
a  hollow  block  of  cast-iron,  in  the  cavity  of  which  the  reservoir 
of  the  manometer  is  situated.  On  one  side  is  a  small  wheel  by 
which  a  cylindrical  plunger,  passing  through  a  long  box  stuffed 
with  leather,  may  be  actuated  for  the  purpose  of  regulating  the 
applied  pressure  or  of  bringing  the  mercury  meniscus  in  the 
stem  of  the  manometer  upon  any  division  mark  determined  in 
advance.  This  pressure  was  calculated  from  the  known  com- 
pressibility of  nitrogen. 

On  the  left  hand  of  the  figure  is  another  massive  hollow 
block  carrying  a  manometer,  within  which  is  the  gas  to  be  com- 
pared with  nitrogen.  This  part  is  more  bulky  than  the  former, 
and  as  a  whole  similar  to  the  apparatus  described  in  my  first 
memoir.  Indeed,  the  experiments  then  treated  might  in  any 
case  be  repeated  with  it.  The  difference  lies  merely  in  details 
of  construction,  and  principally  in  the  disposition  of  the  stop- 
cocks. Only  the  right  half  of  this  large  block  is  to  be  used  in 
the  experiments  with  which  we  are  here  concerned.  The  left 
half  of  this  part  of  the  figure,  carrying  a  lid  with  three  bolts, 
may  be  overlooked.  In  the  earlier  manometric  experiments 
the  lower  end  of  the  hollow  steel  filament  which  ran  to  the  top 
of  the  mine  shaft  was  here  affixed.  [See  couplings  attached.] 

*In  the  Comptes  Eendus,  April  12,  1880,  I  showed  that  under  the  influ- 
ence of  pressure  applied  in  the  interior  only  these  manometers  are  not 
subject  to  an  increase  of  volume  serious  enough  to  make  special  corrections 
necessary. 

16 


THE    LAWS    OF    GASES 


FIG.  1.— APPARATUS  FOR  THE  COMPRESSION  OF  GASES  AT  DIFFERENT  TKMPKRATCRES 

B 


MEMOIRS    ON 

If  the  observations  are  to  be  made  at  atmospheric  tempera- 
tures, the  manometer  containing  the  second  gas  is  jacketed  in 
exactly  the  same  way  as  the  nitrogen  manometer.  If,  however, 
the  observations  are  to  be  made  at  higher  temperatures,  the 
glass  tube  with  circulating  water  is  replaced  by  a  rectangular 
trough,  or  vapor  bath,  supported  on  three  iron  columns,  screwed 
to  the  lid  of  the  same  block  of  iron  which  holds  the  manometer. 
For  this  reason  the  lid  is  circular  and  a  little  too  large,  jutting 
out  slightly  beyond  the  block  to  which  it  is  bolted. 

The  trough  was  cast  of  a  single  piece  of  brass.  On  opposed 
faces  it  is  provided  with  two  long  and  narrow  windows,  closed 
with  plate-glass  held  in  place  by  brass  plates  suitably  screwed 
to  the  sides  of  the  trough.  The  top  is  closed  with  a  square 
brass  lid,  also  secured  in  place  with  bolts.  To  this  is  screwed  a 
vertical  condenser,  the  purpose  of  which  is  to  liquefy  all  escap- 
ing vapor  and  to  return  it  to  the  trough. 

The  condenser  also  carries  the  slide  of  an  agitator  or  stirring 
device  for  equalizing  the  temperature  of  any  liquid  in  the 
trough. 

Temperatures  may  be  read  off  on  the  thermometer  inserted 
through  and  supported  by  the  lid.  As  is  seen,  the  trough  is 
very  solidly  put  together.  It  could,  if  necessary,  resist  great  ex- 
ternal pressures  or  be  used  for  experiments  in  vacua.  The  glass 
plates  were  not  fastened  with  red -lead  cement,  as  is  usually 
done,  but  the  hermetic  seal  was  made  by  aid  of  thick  plates  of 
vulcanized  rubber.  I  cannot  recommend  this  adjustment  too 
highly,  as  it  is  more  convenient  and  more  quickly  put  together 
than  a  red-lead  joint  and  much  less  liable  to  break  the  plate- 
glass  windows  throughout  the  limits  of  temperature  within 
which  india-rubber  can  be  employed.  With  water  at  100°  this 
method  of  sealing  leaves  nothing  to  be  desired. 

The  stem  of  the  manometer  of  crystal  glass  passes  through 
the  bottom  of  the  trough.  The  joint  is  easily  made  by  aid  of  a 
tubulure  and  a  perforated  cork  sliding  on  the  stem.  It  may 
also  be  made  with  a  stuffing-box.  In  the  actual  experiments  I 
prefer  the  first  method,  which  is  more  simple  and  gives  a  good 
hermetic  joint  when  the  necessary  precautions  are  taken,  the 
stem  of  glass  being  made  to  pass  through  exactly  at  the  centre 
of  the  tubulure  which  holds  the  cork.  The  trough,  being  ad- 
justable by  aid  of  double  nuts  on  the  columns,  easily  admits  of 
any  desirable  change  of  position.  One  of  the  columns  carries 

18 


THE    LAWS    OF    GASES 

a  movable  ring-burner,  through  the  centre  of  which  the  stem 
of  the  manometer  passes.  The  crown  of  flame  thus  obtained 
suffices  to  heat  the  liquid  in  the  trough  to  any  required  de- 
gree. 

The  two  parts  of  the  machine  are  connected  by  a  short 
tube  of  steel.  The  apparatus  on  the  left  communicates  with 
the  mercury  pump  mentioned  in  my  first  memoir  through  a 
somewhat  longer  piece  of  the  same  steel  tubing.  As  the 
pump  has  been  already  described,  it  needs  no  further  consid- 
eration here. 

The  two  couplings  or  stopcocks  seen  near  the  bottom  of  the 
apparatus  on  the  left  of  the  figure  serve  to  put  into  commu- 
nication different  parts  of  the  apparatus,  either  with  them- 
selves or  with  the  pump,  or  to  interrupt  these  communications. 
There  is  still  a  third  coupling  in  the  extreme  left  of  the  figure, 
but  this  is  not  essential  in  the  actual  experiments. 

The  whole  apparatus  is  fixed  to  a  heavy  block  of  wood  by  aid 
of  flanges  of  iron,  which  I  have  omitted  in  the  figure.  The 
wooden  block  in  turn  is  secured  to  a  truck  with  four  rollers  of 
cast-iron  ;  this  allows  an  easy  motion  of  the  whole  apparatus, 
whose  weight  is  quite  considerable.  Four  strong  levelling 
screws  were  provided  for  adjusting  the  stems  of  the  manometers 
vertically,  giving  to  the  whole  mechanism  additional  stability. 


METHOD   OF    EXPERIMENTATION 

Having  partially  filled  the  apparatus  with  pure  and  dry 
mercury,  the  nitrogen  manometer  is  first  installed,  and  there- 
after the  second  manometer  provided  with  its  trough.  As  the 
latter  piece  is  very  heavy,  it  would  be  difficult  to  adjust  it  man- 
ually without  accident.  I  therefore  had  a  double  differential 
pulley  attached  to  the  ceiling  of  my  laboratory,  permitting  me 
to  accomplish  this  operation  easily  and  without  danger.  Hav- 
ing completed  the  adjustment  of  the  apparatus,  mercury  is 
injected  by  the  pump  until  this  liquid  shows  itself  in  the 
steins  of  the  manometers.  The  stopcock  on  the  left  is  now 
closed,  while  additional  pressure  is  applied  through  the  small 
hand-wheel,  the  stopcock  on  the  right  being  left  open. 

To  begin  the  measurements,  the  water  in  the  trough  is 
heated  to  the  temperature  selected,  and  the  necessary  con- 
stancy of  temperature  is  maintained  by  suitably  regulating 

19 


UNIVERSITY  ] 


MEMOIRS    ON 

the  flow  of  gas  and  the  distance  of  the  burner  from  the 
bottom  of  the  trough.  This  operation  unfortunately  is  often 
very  prolonged,  particularly  at  the  higher  temperatures.  Dur- 
ing the  whole  time  the  stirring  device  must  be  kept  in  uni- 
form action. 

When  constancy  of  temperature  has  been  reached,  a  heavy 
table  of  wood  is  placed  facing  the  apparatus,  and  two  telescopic 
sights,  fixed  to  the  table,  are  directed  to  the  meniscuses  in 
the  two  manometers  respectively.  Thereupon  an  assistant,  by 
means  of  the  hand-wheel,  brings  the  mercury  successively  on 
the  division  lines  of  the  nitrogen  manometer  corresponding 
to  the  pressures  calculated  in  advance.  The  observer  at  the 
telescopes  registers  the  indications  of  the  two  manometers 
simultaneously  with  those  of  the  thermometer  of  the  trough 
and  of  the  jacket  of  water  circulating  around  the  nitrogen 
manometer. 

As  to  the  latter,  observation  is  made  very  simply  by  placing 
a  white  screen  behind  the  tube,  and  always  bringing  the  base 
of  the  meniscus  upon  a  division  mark  of  the  scale.  To  read 
the  other  manometer,  a  luminous  background,  preferably  the 
ground-glass  globe  of  a  gas-lamp,  is  placed  at  some  distance 
behind  the  posterior  window.  The  reading  of  the  summit  of 
the  meniscus  is  then  observed,  well  marked  by  its  demarcation 
from  the  bright  field.  In  estimating  volumes  with  the  aid  of 
a  prepared  calibration-table,  allowance  is  made  for  this  differ- 
ence of  positions  of  the  meniscuses  in  the  readings. 


METHOD    OF   CALCULATION 

The  experiments  which  I  have  made  with  the  different  gases 
are  all  comprised  between  30  and  420  atmospheres,  and  between 
atmospheric  temperatures  and  100°  C. 

Each  gas  was  studied  in  two  series  of  observations.  With 
the  first  manometer  the  experiments  were  carried  as  far  as  100 
or  130  atmospheres ;  with  the  second  I  proceeded  from  100  or 
130  atmospheres  as  far  as  420  atmospheres.  In  this  way  too 
great  a  reduction  of  the  volume  of  gas  is  avoided. 

The  measurement  of  pressure  given  by  the  nitrogen  manom- 
eter was  also  carried  out  with  two  pieces  of  apparatus  for  like 
reasons. 

This  procedure  renders  the  measurement  of  volume  more 

20 


THE    LAWS    OF    GASES 

exact,  but  it  has  the  drawback  of  presenting  difficulties  in 
recording  the  indications  of  the  two  manometers  and  in  reduc- 
ing them  to  a  single  series.  I  made  this  reduction  by  two  dif- 
ferent methods,  corroborating  them  as  I  shall  indicate  below. 

The  curves  representing  the  results  have  been  constructed  as 
follows  :  the  abscissas  are  laid  oil  proportional  to  the  pressures, 
millimetres  of  length  corresponding  to  meters  of  mercury;  the 
lengths  of  the  ordinates  are  proportional  to  the  corresponding 
values  of  the  products  pv  of  pressure  and  volume. 

All  the  isotherms  for  the  same  gas  at  the  different  tempera- 
tures refer  to  the  same  gaseous  mass ;  in  other  words,  the  ma- 
nometers, after  once  being  charged  with  a  given  gas,  were  used 
in  the  experiments  throughout  all  temperatures  without  taking 
the  apparatus  apart.  To  record  these  families  of  curves  as  a 
whole,  I  made  use  of  the  following  two  procedures  :  Consider 
any  particular  curve.  Supposing  that  the  first  manometer 
has  furnished  the  products  pv  as  far  as  130  atmospheres,  for 
example,  and  the  second  as  far  as  120  atmospheres,  deduce 
from  the  curve  constructed  up  to  130  atmospheres  the  value 
of  pv  at  120  atmospheres.  All  the  numbers  furnished  by  the 
vsecond  manometer  are  now  multiplied  by  the  ratio  of  the  value 
of  pv  at  120  atmospheres  taken  from  the  first  curve  to  that 
of  the  same  product  furnished  by  the  second  manometer  at 
the  same  pressure.  This  factor,  once  calculated,  is  sufficient  to 
co-ordinate  the  relative  curves  at  all  temperatures,  on  condi- 
tion, let  it  be  well  understood,  that  the  series  which  are  thus 
co-ordinated  have  been  made  with  each  manometer  at  exactly 
the  same  temperature.  These  circumstances  were  always  real- 
ized to  about  1°  C.,  and  the  coefficient  calculated  for  one  of  the 
curves  has  always  made  the  others  agree.  To  insure  greater 
accuracy  I  computed  the  coefficient  for  all  the  temperatures 
and  selected  the  mean  value.  Thereafter  I  proceeded  as  fol- 
lows :  Suppose  the  gas  introduced  successively  into  the  two 
manometers  rigorously  at  the  same  temperatures  and  at  the 
same  pressure.  It  would  then  obviously  be  sufficient  to  mul- 
tiply all  the  products  pv  furnished  by  the  second  manometer 
by  the  ratio  of  the  total  volume  of  the  first  manometer  to  that 
of  the  second.  In  reality,  however,  it  was  necessary  to  make 
a  small  correction,  due  to  the  difference  of  temperatures  and 
of  pressures  at  which  the  manometers  were  charged;  but  this 
correction  was  in  all  cases  very  small.  The  coefficients  deter- 

21 


MEMOIRS    ON 

mined  in  this  way  agreed  with  sufficient  accuracy  with  those 
determined  by  the  first  procedure.  They  were  usually  found 
to  be  equal  to  about  one  per  cent.,  and  the  mean  was  taken. 
Frequently  the  agreement  was  even  within  these  limits. 

Finally  the  curves  drawn  to  the  scale  which  I  have  given 
above  were  reduced  to  one-third  of  their  original  dimensions, 
which  far  exceeded  the  usual  size  for  publication. 

The  observations  furnished  at  the  nitrogen  manometer  were 
reduced  in  the  following  way  :  A  table  of  products  pv  was 
first  prepared  by  the  aid  of  my  earlier  researches,  in  which  the 
initial  volume  is  considered  identical  with  that  of  the  manom- 
eter, and  the- initial  pressure  that  under  which  it  was  charged. 
Therewith  a  large  curve  was  constructed  by  laying  oif  volumes 
along  the  abscissas  and  the  values  of  pv  along  the  ordinates. 
From  this  I  deduced  the  values  of  pv  for  the  volumes  corre- 
sponding to  the  scale  marks  on  the  nitrogen  manometer,  up  to 
which  the  mercury  meniscus  was  forced.  Dividing  these  val- 
ues by  the  corresponding  volumes  deduced  from  the  tables  of 
calibration,  the  pressure-values  sought  are  obtained.  Thus  it 
is  supposed  that  the  reading  is  made  at  the  same  temperature 
as  that  at-  which  the  manometer  was  charged  at  normal  press- 
ure. Hence  the  correction  relative  to  the  difference  of  tem- 
perature is  always  very  small.  I  have  also  computed  the 
pressures  by  another  method,  which  gave  me  essentially  the 
same  results.  To  corroborate  the  whole  I  placed  the  two  ni- 
trogen manometers  simultaneously  upon  the  pressure  appara- 
tus, and  I  thus  found  that  throughout  the  coincident  part  of 
their  registry — i.  e.,  between  about  100  and  130  atmospheres — 
they  gave  the  same  results  to  about  half  an  atmosphere. 

It  has  just  been  shown  that  in  making  the  calculations 
needed  for  joining  the  curves  it  is  necessary  to  know  at  what 
temperature  and  at  what  pressure  the  manometers  were  charged 
with  gas.  The  experiments  were  so  conducted  that  the  small 
cylinder  which  ends  off  the  reservoirs  of  the  manometers  be- 
low was  submerged  in  mercury  at  the  moment  at  which  its 
pressure  and  its  temperature  were  identical  with  that  of  the 
atmosphere,  although  communication  with  the  gas  supply 
had  not  yet  been  cut  off.  While  the  small  cylinder  was  thus 
plunged  in  the  mercury  bath,  it  was  provided  with  a  small 
iron  thimble,  kept  in  place  by  suspension  from  two  springs. 
In  this  way  the  manometer  could,,  be  removed  or  placed  upon 

22 


THE    LAWS    OF    GASES 

the  apparatus,  the  efflux  point  remaining  plunged  in  the  mer- 
cury within  the  thimble. 

As  a  general  thing,  three  series  of  operations  were  made  with 
each  gas  and  with  each  manometer.  Having  thus  established 
the  accordance  of  a  large  number  of  series,  I  selected  the  one 
which  seemed  to  have  been  made  under  the  most  satisfactory 
conditions. 

I  took  every  feasible  precaution  to  have  the  gases  as  pure,  as 
free  from  air,  and  as  dry  as  possible.  For  the  case  of  carbon 
dioxide,  in  particular,  the  gas  was  tested  even  in  the  manometer 
at  the  end  of  the  experiments.  The  results  given  below  refer 
to  a  gas  which  left  a  residue  of  only  5  parts  in  lt)00  in  the  lower- 
pressure  manometer  and  2  parts  in  1000  in  the  other.  All  the 
gases,  without  exception,  were  first  dried  in  concentrated  sul- 
phuric acid,  thereafter  in  a  desiccator  filled  with  broken  glass 
mixed  with  anhydrous  phosphoric  acid. 


NUMERICAL    RESULTS 

The  numerical  results  contained  in  the  following  tables  were* 
obtained  from  the  curves  which  have  already  been  discussed. 
For  ethylene  and  carbon  dioxide,  in  which  the  variations  of 
pressure  are  exceedingly  abrupt,  I  have  given  the  values  of 
pv  in  intervals  from  10  to  10  meters  of  mercury ;  for  the  other 
gases,  in  intervals  of  x>0  meters  only.     The  first  horizontal  row 
shows  the  temperatures  at  which  the  observations  were  made. 
The  corresponding  pressures  are  contained  in  the  first  vertical 
column. 

In  case  of  marsh  gas  (methane)  data  are  given  only  up  to- 
300  atmospheres.  This  gas  was  actually  studied  in  certain 
series  as  far  as  420  atmospheres,  like  the  others  ;  but  an  error 
appeared  in  the  values  of  the  coefficient  for  co-ordinating  these 
curves  which  increased  to  more  than  three  per  cent.,  and  which 
I  have  not  been  able  to  explain  to  my  own  satisfaction.  I 
therefore  prefer  to  give  the  data  of  the  first  series  only,  which 
showed  sufficient  accordance  throughout. 


MEMOIRS    ON 


VALUES    OF    pv    FOR    NITROGEN 


Meters,  Hg. 

17.7° 

30.1° 

50.4° 

75.5° 

100.1° 

30 

2745 

2875 

3080 

3330 

3575 

40 

2740 

2865 

3085 

3340 

3580 

60  • 

2740 

2875 

3100 

3360 

3610 

80 

2760 

2895 

3125 

3400 

3650 

100 

2790 

2930 

3170 

3445 

3695 

120 

2835 

2985 

3220 

3495 

3755 

140 

£890 

3040 

3275 

3550 

3820 

1(50 

2950 

3095 

3335 

3615 

3880 

180 

3015 

3150 

3390 

3675 

3950 

200 

3075 

3220 

3465 

3750 

4020 

220 

3140 

3285 

3530 

3820 

4090 

240 

3215 

3360 

3610 

3895 

4165 

260 

3290 

3440 

3685 

3975 

4240 

280 

3370 

3520 

3760 

4050 

4320 

300 

3450 

3600 

3840 

4130 

4400 

320 

3525 

3675 

3915 

4210 

4475 

VALUES    OF    pv    FOR    HYDROGEN 


Meters,  Hg. 

17.7° 

40.4° 

60.4° 

81.1° 

100.1° 

30 

2830 

3045 

3235 

3430 

3610 

40 

2850 

3065 

3240 

3445 

3625 

60 

2885 

3110 

3295 

3500 

3680 

80 

2935 

3155 

3340 

3550 

3725 

100 

2985 

3200 

3400 

3620 

3780 

120 

3040 

3255 

3455 

3665 

3830 

140 

3080 

3300 

3500 

3710 

3880 

160 

3135 

3360 

3560 

3775 

3945 

180 

3185 

3420 

3620 

3830 

4010 

200 

3240 

3465 

3685 

3870 

4055 

220 

3290 

3520 

3725 

3930 

4110 

240 

3340 

3570 

3775 

3980 

4160 

260 

3400 

3625 

3830 

4040 

4220 

280 

3450 

3675 

3880 

4090 

4275 

300 

3500 

3730 

3935 

4140 

4325 

320 

3550 

3780 

3990 

4200 

4385 

<•• 

1T                ISITY] 

THE    LAWS    OF    GASl^^i 

MARSH    GAS     (METHANE) 

Meters,  Hg. 

14.7° 

29.5° 

40.6° 

60.1° 

79.8° 

100.1° 

TO 

2580 

2745 

2880 

HI  00 

*J  \J 

40 

2515 

/V   i  TT«J 

2685 

>vOOV/ 

2830 

tJ  X  \J\J 

3060 

3290 

3505 

i    60 

2400 

2590 

2735 

2995 

3230 

3460 

80 

2315 

2515 

2675 

2950 

3195 

3440 

100 

2275 

2480 

2640 

2935 

3180 

3435 

120 

2245 

2465 

2635 

2925 

3180 

3440 

140 

2260 

2480 

2655 

2940 

3190 

3460 

160 

2300 

2510 

2685 

2975 

3220 

3490 

180 

2360 

2560 

2730 

3015 

3260 

3525 

200 

2425 

2615 

2780 

3065 

3305 

3575 

220 

2510 

2690 

2840 

3125 

3360 

3625 

230 

2560 

2730 

2880 

3150 

3385 

3650 

M.IIg. 

16.3° 

\ 

20.3° 

•ALUEf 

30.1° 

5  OF  j 
40.0° 

PV  FO 

50.0° 

R  ETI 

60.0° 

IYLEN 
70.0° 

E 
79.9° 

89.9° 

100.0° 

25 

01  /LA 

991  ^ 

9360 

/CO 

30 

/V  J-TTV/ 

1950 

v/v'-L  tJ 

2055 

4vO  vVr 

2220 

2410 

2580 

2715 

2865 

2970 

3090 

3225 

40 

1350 

1700 

1900 

2145 

2335 

2510 

2675 

2825 

2960 

3110 

50 

850 

1075 

1540 

1860 

2100 

2315 

2490 

2670 

2825 

2980 

60 

810 

900 

1190 

1535 

1875 

2100 

2310 

2500 

2680 

2860 

70 

880 

945 

1110 

1340 

1675 

1920 

2150 

2365 

2560 

2740 

80 

975 

1030 

1130 

1285 

1535 

1780 

2015 

2240 

2450 

2640 

90 

1065 

1115 

1195 

1325 

1510 

1710 

1930 

2160 

2375 

2565 

100 

1150 

1200 

1275 

1380 

1535 

1690 

1895 

2105 

2335 

2515 

110 

1240 

1280 

1360 

1460 

1590 

1725 

1915 

2705 

2310 

2490 

120 

1325 

1370 

1440 

1540 

1660 

1780 

1950 

2115 

2305 

2470 

130 

1415 

1455 

1525 

1620 

1725 

1840 

2000 

2150 

2320 

2480 

140 

1505 

1540 

1610 

1700 

1800 

1910 

2060 

2190 

2350 

2505 

150 

1590 

1625 

1690 

1785 

1880 

1990 

2125 

2250 

2390 

2540 

160 

1680 

1715 

1780 

1865 

1960 

2070 

2195 

2310 

2445 

2585 

170 

1770 

1800 

1860 

1950 

2045 

2145 

2265 

2375 

2505 

2640 

180 

1855 

1890 

1945 

2035 

2130 

2225 

2340 

2450 

2565 

2700 

190 

1940 

1975 

2030 

2120 

2210 

2310 

2415 

2525 

2635 

2760 

200 

2030 

2065 

2115 

2200 

2290 

2390 

2490 

2600 

2715 

2835 

210 

2110 

2145 

2200 

2285 

2375 

2470 

2565 

2680 

2790 

2910 

220 

2195 

2225 

2280 

2370 

2460 

2550 

2650 

2760 

2865 

2975 

230 

2280 

2315 

2370 

2460 

2540 

2635 

2730 

2835 

2940 

3050 

240 

2360 

2395 

2450 

2540 

2625 

2720 

2810 

2910 

3015 

3125 

250 

2445 

2480 

2540 

2625 

2710 

2800 

2890 

2990 

3090 

3200 

260 

2530 

2560 

2625 

2710 

2790 

2880 

2980 

3075 

3175 

3275 

270 

2610 

2640 

2710 

2790 

2875 

2965 

3060 

3150 

3240 

3345 

"280 

2695 

2725 

2790 

2875 

2960 

3045 

3140 

3225 

3320 

3420 

290 

2780 

2810 

2875 

2960 

3040 

3125 

3220 

3310 

3400 

3490 

300 

2860 

2890 

2960 

3040 

3125 

3215 

3300 

3380 

3470 

3560 

310 

2945 

2975 

3040 

3125 

3210 

3290 

3385 

3465 

3550 

3635 

320 

3035 

3065 

3125 

3200 

3285 

3375 

3470 

3545 

3625 

3710 

MEMOIRS    ON 


M.Hg. 

VAl 

18.2° 

LUES 
35.1° 

OF  pv 

40.2° 

FOR 

50.0° 

CARBC 
60.0° 

)N  DIOXIDE 
70.0°  80.0° 

90.2° 

100.0° 

30 

Liquid 

2360 

2460 

2590 

2730 

2870 

2995 

3120 

3225 

40 

a 

2065 

2195 

2370 

2535 

2700 

2840 

2985 

3105 

50 

tf 

1725 

1900 

2145 

2330 

2525 

2685 

2845 

2980 

60 

a 

1170 

1500 

1860 

2115 

2340 

2530 

2705 

2860 

70 

« 

725 

950 

1530 

1890 

2155 

2380 

2570 

2750 

80 

625 

750 

825 

1200 

1650 

1975 

2225 

2440 

2635 

90 

685 

810 

865 

1080 

1430 

1775 

2075 

2315 

2530 

100 

760 

870 

920 

1065 

1315 

1630 

1940 

2200 

2425 

110 

825 

930 

980 

1090 

1275 

1550 

1845 

2105 

2325 

120 

j  890 

995 

1045 

1140 

1285 

1510 

1775 

2030 

2260 

130 

955 

1060 

1115 

1190' 

1315 

1505 

1735 

1980 

2190 

140 

1020 

1120 

1175 

1250 

1360 

1525 

1715 

1950 

2160 

150 

1080 

1180 

1235 

1310 

1415 

1560 

1725 

1945 

2135 

160 

1145 

1250 

1300 

1370 

1465 

1600 

1745 

1960 

2130 

170 

1210 

1310 

1360 

1430 

1520 

1645 

1780 

1975 

2135 

180 

1275 

1375 

1410 

1485 

1580 

1700 

1825 

2000 

2150 

190 

1340 

1440 

1480 

1550 

1645 

1760 

1875 

2035 

2180 

200 

1405 

1500 

1550 

1615 

1705 

1810 

1930 

2075 

2215 

210 

1470 

1565 

1610 

1675 

1765 

1870 

1980 

2120 

2250 

220 

1530 

1625 

1670 

1740 

1825 

1925 

2040 

2160 

2290 

230 

1590 

1690 

1730 

1800 

1890 

1990 

2090 

2210 

2340 

240 

1650 

1750 

1790 

1865 

1950 

2045 

2150 

2260 

2390 

250 

1710 

1815 

1855 

1925 

2010 

2100 

2205 

2320 

2435 

260 

1770 

1870 

1920 

1985 

2070 

2165 

2265 

2375 

2490 

270 

1830 

1935 

1975 

2050 

2130 

2220 

2320 

2435 

2540 

280 

1890 

2000 

2040 

2110 

2190 

2285 

2380 

2490 

2600 

290 

1950 

2060 

2100 

2170 

2260 

2340 

2440 

2550 

2655 

300 

2010 

2120 

2160 

2235 

2320 

2405 

2500 

2605 

2715 

310 

2070 

2180 

2220 

2300 

2375 

2460 

2560 

2660 

2765 

320 

2135 

2240 

2280 

2360 

2440 

2525 

2620 

2725 

2830 

The  curves  given  in  figures  2,  3,  4,  5,  6,  represent  these  results 
comprehensively.  In  those  relative  to  nitrogen,  to  hydrogen, 
and  to  marsh  gas  a  part  of  the  ordinate  lengths  has  been  sup- 
pressed. It  is  therefore  necessary  to  reproduce  this  inferential- 
ly  with  the  aid  of  the  numbers  given  at  the  origin. 


EXAMINATION   AND   DISCUSSION   OF  THE   RESULTS 

An  inspection  of  the  curves  shows  at  once  that  the  families 
may  be  referred  to  two  extreme  and  to  certain  intermediate 
types.  For  hydrogen  all  the  lines  are  appreciably  parallel  and 

26 


THE    LAWS    OF    GASES 

straight  at  all  the  temperatures  at  which  experiments  were 
made.  This  invariability  in  the  form  of  the  curves  seems 
to  indicate  that  this  gas  has  reached  a  limiting  state  charac- 
terized by  their  direction.  At  all  the  temperatures  which  I 
investigated  the  values  of  pv  increase  in  their  variation  with 
pressure. 

Carbon  dioxide  and  ethylene  form  the  contrasting  type.    The 
products  pv  at  first  decrease  very  rapidly,  reach  a  minimum, 


20  40  60  80  100  120  140  160  180  200  220  240  260  280 


FIG.  2. — ISOTHERMS  (pv)  FOR  NITROGEN 


and  thereafter  increase  indefinitely.  These  variations  of  pv, 
very  rapid  at  temperatures  near  the  critical  point,  show  a 
marked  diminution  when  temperature  rises.  The  point  of  the 
curve  at  which  the  ordinate  is  a  minimum  moves  regularly 
away  from  the  origin,  and  the  locus  traced  comes  out  very  clearly 
on  inspection  of  the  curves.  The  minimum  seems  to  move  away 
from  the  origin  less  rapidly  after  passing  a  certain  temperature  ; 
after  which  it  apparently  retrogrades.  At  least,  this  takes  place 
in  marsh  gas  and  nitrogen.  Now  these  gases  which  constitute 
the  intermediate  type  are  at  like  temperatures  much  more  dis- 
tant, from  their  critical  state  than  ethylene  or  carbon  dioxide. 
For  the  case  of  nitrogen  and  marsh  gas  the  displacement  of  the 
minimum  ordinate  appears  much  less  sharply  defined  than  for 
the  other  gases,  for  the  reason  that  when  curvature  diminishes, 
the  position  of  this  ordinate  is  much  more  difficult  to  determine 
sharply.  I  subjoin  a  table  for  carbon  dioxide  and  ethylene, 

27 


MEMOIRS    ON 

showing  at  what  pressure  in  meters  of  mercury  the  ordinate  is 
a  minimum  at  different  temperatures  : 


CARBON  DIOXIDE 

ETHYLENE 



— 

16.3° 

55" 



— 

20.3 

60 

35.1° 

70* 

30.1 

70 

40.2 

80 

40.0 

80 

50.0 

98 

'50.0 

88 

60.0 

115 

60.0 

95 

\70.0 

130 

70.0 

100 

80.0 

140 

79.9 

105 

90.2 

150 

89.9 

115 

100.0 

160 

100.0 

120 

The  curves  for  carbon  dioxide  and  ethylene  may  advan- 
tageously be  considered  by  themselves  for  the  time  being ;  be- 
cause of  the  larger  variations  of  compressibility  involved,  they 


44 


42 


26 


40 


38 


36 


34 


32 


,30 


28  i 


20  40  60  80  100  120  140  160  180  200  220  240  260  280  300  320 

FIG.  3. — ISOTHERMS  (pv)  FOR  HYDROGEN 

are  more  suitable  than  the  others  for  the  demonstration  of  the 
general  laws  of  these  variations.  Let  the  curves  for  carbon 
dioxide  be  taken  first.  It  is  obvious  at  the  outset  that  at  tem- 
peratures in  the  neighborhood  of  the  critical  point  the  initial 
branches  of  the  curves,  or  those  which  precede  the  minimum 
ordinate,  are  concave  towards  the  axis  of  pressure.  The  con- 

28 


THE    LAWS    OF    GASES 

cavity  is  well  marked,  and  appears  to  be  prolonged  quite  into 
the  region  of  small  pressures.  This  is  indicated  by  the  dotted 
lines  which  represent  the  phenomenon  approximately,  at  press- 
ures lower  than  those  at  which  the  experiments  began. 

To  construct  these  parts  of  the  curve  I  simply  determined 


20    '40      60     80     100    120    140    160    180   200    220   240    260   280   300    320 
FIG.  4. — ISOTHERMS  (pv)  FOR  ETHYLENE 

the  point  of  departure  corresponding  to  normal  pressure,  which 
was  found  without  difficulty,  since  I  knew  the  volume  of  carbon 
dioxide  for  the  particular  pressure  and  temperature  at  which 
the  manometer  was  charged  with  gas.  From  this  I  deduced 
the  volume  occupied  by  the  gas,  and  consequently  the  value  of 


MEMOIRS    ON 

pv,  at  the  same  pressure  for  all  the  temperatures,  in  virtue  of 
the  values  of  the  coefficient  of  expansion  of  carbon  dioxide, 
given  a  long  time  ago  in  my  own  papers,  for  temperatures 
between  0°  and  100°  and  under  normal  pressure.  Thereupon  I 
joined  the  points  of  departure  so  obtained  with  the  first  points 
of  the  continuous  curves,  allowing  myself  to  be  guided  by  their 


20  40   60   80  100  120  140  160  180  200  220  240  260  230  300  320 

YIG.  5. — ISOTHERMS  (pv)  FOR  CARBON  DIOXIDE 

general  trend.  Similar  dotted  lines  were  drawn  for  nitrogen 
and  hydrogen,  but  not  for  ethylene  and  methane,  since  I  lacked 
data  as  to  their  dilatation. 

To  return  from  this  digression  to  the  general  form  of  the 
curves,  I  may  point  out  that  the  concavity  observed  in  the 
initial  branches  which  is  presented  in  the  case  of  ethylene, 

30 


THE    LAWS    OF    GASES 


occurs  also,  I  might  almost  say  a  fortiori,  in  the  results  which 
Regnault  investigated  as  far  as  28  atmospheres.  In  fact,  these 
data  were  obtained  at  temperatures  lower  than  those  from  which 
I  started — i.  e.,  lower  than  35°  for  carbon  dioxide. 

The  concavity  specified  vanishes  pretty  rapidly  when  tempera- 
ture rises.  At  50°  0.  it  is  no  longer  apparent,  and  the  curve  only 
presents  the  convexity  which  produces  the  minimum  of  pv. 

For  gases  other  than  ethylene  and  carbon  dioxide,  the  con- 
cavity has  entirely  disappeared  even  at  ordinary  temperatures. 
This  form  of  curve  for  the  lower  pressures,  for  the  moment  at 


36 


32 


30 


28 


26 


24 


22 


•20   40    60    80   "100   120   140   '160   180   230   220   240 

FIG.  6. — ISOTHERMS  (pv)  FOR  MARSH  GAS 

least,  does  not  command  much  attention ;  but  it  is  quite  dif- 
ferent in  those  parts  of  the  curves  which  follow  the  minimum 
ordinate,  and  throughout  which  pv  increases  indefinitely.  For 
temperatures  in  the  neighborhood  of  the  critical  point,  the 
curve  turns  rapidly  after  passing  the  ordinate  in  question,  and 
changes  almost  at  once  into  a  line  which  is  very  nearly  straight. 
Some  points  seem  to  indicate  traces  of  concavity,  so  vaguely, 
however,  as  to  be  referable  to  errors  of  observation. 

As  temperature  rises  the  convexity  of  the  curves  diminishes 
very  rapidly,  and  the  general  aspect  of  the  families  of  curves 
shows  an  unmistakable  tendency  to  slope  upward  and  to  change 
to  straight  lines  throughout  their  extent.  The  occurrence  of 
minimum  ordinates  thus  gradually  ceases. 

31 


MEMOIRS    ON 

True,  this  tendency  is  indicated  clearly  only  in  the  isotherms 
of  carbon  dioxide  and  of  ethylene.  If,  however,  one  calls  to 
mind  that  hydrogen  is  at  ordinary  temperatures  in  a  thermal 
state,  which  the  two  gases  specified  reach  at  very  much  higher 
temperatures ;  that  for  hydrogen  the  transformation  in  ques- 
tion is  actually  complete  at  ordinary  temperatures,  continuing 
in  the  same  sense  up  to  100°  without  showing  the  slightest 
trace  of  any  superimposed  deformation  ;  if,  finally,  one  adds 
the  evidence  obtained  from  the  curves  for  methane  and  nitro- 
gen which  make  up  the  intermediate  type,  then  the  general 
features  of  these  gaseous  phenomena  become  strikingly  appar- 
ent. Indeed,  I  would  insist  on  this  point  of  view  (the  conse- 
quences of  which  will  be  shown  below),  that  not  only  do  the 
curves  straighten  out  for  all  gases  in  such  a  way  as  to  reproduce 
the  case  of  hydrogen  at  sufficiently  high  temperatures — i.e., 
in  a  way  to  present  values  of  pv  continually  increasing  with 
pressure — but  that  they  really  tend  to  become  straight  lines 
throughout  their  whole  extent. 

For  hydrogen  the  occurrence  of  straight  isotherms  is  as 
completely  verified  as  the  accuracy  of  the  experiments  permits 
up  to  100  atmospheres  about  and  from  ordinary  temperatures 
onward.  At  smaller  pressures,  a  trace  of  concavity  seems  still 
to  cling  to  the  curves.  This  is  much  less  discernible  at  100°, 
if  it  be  not  altogether  wiped  out. 

The  concavity  of  the  curves  for  nitrogen  is  clearly  marked 
at  ordinary  temperatures,  but  it  is  much  less  accentuated  at 
100°,  where  the  rectilinear  portions  are  already  apparent. 

Another  fact  not  less  important  (as  will  appear  below)  is  this, 
that  the  curves  in  their  rectilinear  parts  are  nearly  parallel ; 
parallel  in  such  a  way,  moreover,  that  to  obtain  the  general 
direction  of  these  lines — a  characteristic  for  each  gas — it  is 
sufficient  to  construct  one  of  them  near  the  critical  point. 
Under  critical  conditions  the  lines  become  straight  almost 
immediately  after  leaving  the  minimum  ordinate.  Neverthe- 
less, it  would  be  hazardous  to  affirm  that  these  lines  are  abso- 
lutely parallel ;  they  seem  rather  to  merge  gradually  into 
straight  lines,  being  asymptotic  to  a  direction  which  differs 
very  little  in  all  the  cases  for  the  portion  already  sensibly 
straight  in  the  curves  constructed. 

The  endeavor  must  now  be  made  to  unravel  general  laws 
relative  to  the  variation  of  compressibility  with  temperature. 

32 


THE    LAWS    OF    GASES 

AVe  have  seen  that  for  each  gas  there  exists  a  temperature 
beyond  which  pv  increases  continually  with  pressure.  It  is, 
however,  inaccurate  to  state  that  with  increasing  temperature 
the  gas  continues  to  diverge  more  and  more  seriously  from  the 
law  of  Mariotte,  in  the  sense  of  being  less  compressible.  The 

contrary  is  the  fact.    Let  the  values  of  the  ratio  -^r-,  be  examined 

p  v 

between  the  limits  p  and  p'  of  pressure  and  at  different  tem- 
peratures. It  follows  from  the  parallelism  of  the  lines  that 
in  passing  from  a  given  temperature  to  another  higher  in  the 
scale  the  values  of  pv  and  p'v'  increase  by  the  same  quantity. 
Hence  the  value  of  the  ratio  increases,  since  it  is  smaller  than 
one. 

All  this  is  clearly  shown  in  the  following  table  containing 

7)V 

values  of  -—  between  100  meters  and  320  meters  of  pressure 
p  v 

and  at  different  temperatures: 


HYDROGEN 

0  C.  RATIO  V?-, 

pv 

17.7 0.830 

40.4 838 

60.4 ' 845 

80.1 853 

100.1  .  .856 


Thus  for  increasing  temperatures  the  gas  expands  more  in 
accordance  with  Mariotte  Js  law,  for  the  simple  reason  that  the 
constant  difference  of  the  products  pv  and  p'v'  is  added  to  the 
greater  and  greater  values  of  the  products.  The  reason  is  not 
that  jov  tends  to  become  constant,  a  result  which  occurs  for  no 
gas  whatever. 

It  is  quite  certain  that,  on  sufficiently  cooling  hydrogen,  this 
gas  would  eventually  contract  more  than  the  law  of  Mariotte 
indicates.  On  increasing  temperature  the  discrepancy  would 
at  first  vanish  and  thereafter  change  sign.  But  the  divergence, 
instead  of  continuing  to  increase  negatively,  would  reach  a 
maximum  value,  after  which  it  would  begin  to  approacli  unity, 
as  is  actually  the  case  in  the  experiments, 
c  33 


MEMOIRS    ON 

Let  the  family  of  curves  relative  to  carbon  dioxide  now  be 
examined  :  They  begin  at  35°  C. — i.e.,  only  a  few  degrees  above 

the  critical  point.     Following  the  values   -,—,  from  degree  to 

degree  between  the  pressure  limits  100  and  120  meters  of  mer- 
cury, for  example,  we  find  the  ratio  smaller  than  unity  at  35°, 
40°,  and  50°.  Above  60°,  on  the  contrary,  the  ratio  exceeds 
unity  ;  after  this  it  evidently  again  becomes  smaller  as  the 
temperature  continually  increases,  and  finally  remains  indefi- 
nitely at  a  point  below  this  value.  Clearly,  therefore,  the 
period  within  which  the  gas  is  more  compressible  than  the  law 
of  Mariotte  asserts  may  be  preceded  by  a  period  where  it  is 
less  so  at  a  lower  temperature.  The  curves  also  show  that  a 

1)V 

pressure  exists  beyond  which  -Lr-l  is  always  smaller  than  unity, 

whatever  be  the  temperature.  If  one  imagines  the  locus  of  the 
points  of  minimum  ordinates  actually  constructed,  and  if  the 
curve  has  itself  a  maximum  abscissa  (I  have  shown  that  this  is 
very  probable),  it  is  beyond  the  pressure  corresponding  to  this 
abscissa  that  the  fact  in  question  becomes  manifest. 

Approaching  the  region  of  lower  pressures  one  observes  simi- 
larly that  a  value  exists  beyond  which  the  primary  period  cor- 

79?^ 

responding  to  —-;  <  1  no  longer  occurs.  The  value  in  ques- 
tion is  the  pressure  at  which  the  gas  liquefies  at  a  temperature 
very  near  the  critical  point.  It  is  the  critical  pressure. 

All  these  results  are  rather  complicated,  although  an  inspec- 
tion of  the  curves  immediately  shows  them  clearly.  They  may, 
however,  be  enunciated  in  a  simpler  form.  Suppose  the  family 
of  curves  divided  into  two  regions  by  the  curve  which  is  the 
locus  of  minimum  ordinates.  The  left-hand  area  will  then 

DV 

comprehend  those  parts  of  the  curves  for  which  --,--,  >  1;  in 
the  right-hand  area,  contrariwise,  we  shall  everywhere  have 

ItV  *DV 

J-i—,  <  1.    In  the  first  region,  —-;  decreases  when  temperature 

increases  ;  in  the  second  the  opposite  is  the  case. 

The  following  table  has  been  computed  from  the  data  for 
carbon  dioxide  to  substantiate  these  results.  It  may  be 
observed  in  passing  that  in  the  second  region  the  effect  of 
temperature  diminishes  whenever  pressure  increases. 

34 


THE    LAWS    OF    GASES 


CARBON   DIOXIDE 


TEMP. 

3QX—10M 

VA 

LUES    OF     - 

pv 

200* 

?V 

140*—  20(W 

18.2°  (Liq.) 



— 

.745 

.726 

.658 

35.1 

3.255 

.833 

.777 

.747 

.670 

40.2 

2.893 

.924 

.783 

.758 

.688 

50.0       " 

1.693 

1.452 

.844 

.774 

.685 

60.0 

1.444 

1.437 

.967 

.797 

.699 

70.0 

1.329 

1.322 

1.069 

.842 

.712 

80.0       " 

1.258 

1.227 

1.131 

.888 

.736 

90.2 

1.214 

1.168 

1.128 

.940 

.761 

100.0       " 

1.172 

1.134 

1.122 

.975 

.782 

The  limits  of  pressure  between  which  ~-;  has  been  calculated 

are  inscribed  at  the  head  of  the  respective  vertical  columns. 
We  may  therefore  summarize  the  role  of  temperature  in  its 
effect  upon  the  compressibility  of  gases  by  the  following  laws  : 

1.  For  pressures  lower  than  the  critical  pressure  and  with  con- 
tinually increasing  temperature,  the  divergence  from  Mariotte's 
law,  positive  at  first  at  sufficiently  low  temperatures,  passes 
through  zero  and  eventually  becomes  negative.     Beyond  a  certain 
negative  value,  however,  the  discrepancy  diminishes  indefinitely 
without  changing  sign. 

2.  For  pressures  between  the  critical  value  and  a  superior 
limit  peculiar  to  each  gas,  the  period  during  which  the  dis- 
crepancy is  positive  is  preceded  at  still  lower  temperatures  by  a 
period  for  which  it  is  negative,  in  such  a  way  that  the  discrepancy 
changes  sign  twice. 

#.  Beyond  the  superior  limit  indicated  in  the  preceding  law 
the  discrepancy  is  negative  at  all  temperatures.  It  diminishes 
in  general  as  temperature  increases,  always  excepting  those  press- 
ures which  are  too  near  the  limit  specified.  In  these  places  the 
variation  is  more  complicated. 

4.  Begond  a  sufficiently  high  temperature  the  law  of  compressi- 
bility of  a  gas  is  represented  by  the  equation  P  (  V—a)  =  const., 
wherein  a  is  the  smallest  volume  to  which  the  gas  can  be  reduced; 
in  other  ivords,  a  is  the  absolute  volume  of  the  constih 

35 


UNIVERSITY 


MEMOIRS    ON 

The  last  law  virtually  states  (as  will  appear  below)  that 
beyond  a  certain  sufficiently  high  temperature  all  the  curves 
become  straight  lines. 

It  goes  without  saying  that  the  departure  from  the  law  of 
Mariotte  here  in  question  refers  to  pressures  arbitrarily  chosen 
within  the  limits  of  pressure  indicated  by  the  laws. 


DILATATION   OF   GASES   AT   HIGH    PRESSURES 

The  data  which  precede  are  evidently  available  for  the  com- 
putation of  the  coefficient  of  expansion  of  a  gas,  even  though 
the  experiments  were  not  specially  directed  towards  this  end. 
True,  results  so  obtained  cannot  have  a  degree  of  precision 
comparable  with  those  investigated  by  the  ordinary  methods  at 
low  pressures  ;  but  the  accuracy  will  nevertheless  be  sufficient 
to  point  out  the  general  features. 

Mere  inspection  of  the  families  of  curves  enables  us  to 
form  a  conception  of  the  remarkable  variation  to  which  the 
dilatation  of  a  gas  is  subject  in  the  neighborhood  of  the  locus 
of  minimum  ordinates;  above  all,  at  temperatures  near  the 
critical  point. 

If  we  reflect  that  for  a  given  pressure  the  length  of  the  ordi- 
nate  is  at  each  temperature  proportional  to  the  volume  of  the 
gas,  it  follows  that  the  dilatation  for  each  pressure  is  conse- 
quently given  by  the  curves.  To  arrive  at  the  general  facts, 
however,  it  is  necessary  to  compare  the  coefficients  of  mean 
expansion  at  different  pressures  between  the  sufficiently  narrow 
limits  of  temperature.  It  is  with  this  end  in  view  that  I  have 
computed  the  table  which  is  about  to  follow. 

7j' 2« 

The  coefficients  of  expansion  inserted  are  the  values  of    //__//\ 

between  the  limits  of  pressure  and  of  temperature  indicated. 
The  volumes  were  deduced  from  the  curves  by  dividing  the 
ordinates  pv  by  the  corresponding  pressure.  It  sufficed  for  this 
purpose  to  take  the  difference  of  ordinates  corresponding  to 
t  and  t'  degrees  at  each  pressure,  to  divide  this  difference  by 

fk\^  1J      -/I??  7?         m-    —    7T 

the  inferior  ordinate  giving  ^— —  or  -    — ,  and  finally  to 

pv  v 

divide  this  result  by  the  difference  of  temperature. 

The  data  thus  obtained  for  carbon  dioxide  and  ethylene 
follow : 


THE    LAWS    OF    GASES 


Pressure 

CAKB 

18°—  35° 

ON  DIOXIDI 
40o_60° 

3 
60°—  80° 

80°—  100° 

40  Meters 

Liquid 

.0074 

.0058 

.0046 

60 

— 

.0196 

.0096 

.0052 

80 

.0113 

.0500 

.0176 

.0089 

100   " 

.0072 

.0217 

.0238 

.0135 

120 

.0062 

.0114 

.0151 

.0123 

140 



.0085 

'.0128 

.0127 

160 

.0043 

.0066 

.0095 

.0108 

180 

— 

.0056 

.0079 

.0087 

•200 

.0039 

.0052 

.0071 

.0072 

220 



.0048 

.0057 

.0063 

240 

.0033 

.0045 

.0051 

.0056 

260 

— 

.0040 

.0045 

.0048 

280 

.0029 

.0039 

.0042 

.0046 

300 

— 

.0038 

.0039 

.0044 

320 

.0025 

.0037 

.0038 

.0040 

ETHYLENE 


Pressure 

200—40° 

40o_60° 

60°—  80° 

80°—  100° 

30  Meters 

.0084 

.0064 

.0046 

.0040 

60 

.0366 

.0178 

.0097 

.0067 

80 

.0121 

.0195 

.0132 

.0088 

100 

.0079 

.0108 

.0121 

.0100 

120 

.0062 

.0075 

.0095 

.0082 

140 

.0048 

.0062 

.0076 

.0068 

160 

.0041 

.0057 

.0061 

.0058 

200 

.0034 

.0043 

.0044 

.0044 

240 

.0030 

.0035 

.0036 

.0034 

280 

.0027 

.0031 

.0030 

.0029 

320 

.0025 

.0027 

.0024 

.0024  - 

If  by  running  along  a  horizontal  column  one  endeavors  to 
find  how  the  coefficient  of  expansion  varies  with  temperature 
at  constant  pressure,  one  observes  a  rather  complex  result  for 
the  values  given  in  the  middle  of  the  table,  which  correspond 
to*  the  neighborhood  of  the  locus  of  minimum  ordinates ;  but 
if  one  considers  only  the  extreme  regions,  regions  which  corre- 
spond to  low  pressures  or  to  pressures  relatively  high,  it  becomes 
easily  manifest  that  the  coefficient  diminishes  regularly  with 
temperature.  Particularly  on  arriving  near  the  limits  of  press- 

37 


MEMOIRS    ON 

lire  will  it  be  observed  that  the  expansion  is  sensibly  propor- 
tional to  the  interval  of  temperature.  This  is  the  case  with 
hydrogen  at  all  pressures. 

Again,  if  in  a  survey  of  the  vertical  columns  of  the  tables  we 
endeavor  to  find  the  variation  of  the  coefficient  of  expansion 
with  pressure  at  a  given  constant  temperature,  we  encounter  a 
clear-cut  law  at  once.  The  coefficient  is  at  first  seen  to  increase 
with  pressure  up  to  a  maximum  value,  and  thereafter  to  decrease 
regularly.  This  maximum  corresponds  very  nearly  to  the 
pressure  for  which  the  ordinate  is  a  minimum.  If  in  place  of 
taking  the  mean  coefficient  between  limits  as  far  apart  as  20° 
the  temperature  interval  t'  —  t  be  more  and  more  diminished, 

the  limiting  value  -j-  -  will  coincide  as  to  the  pressure  position 

of  its  maximum  with  the  same  pressure  which  corresponds  to 
the  minimum  ordinate. 

In  proportion  as  temperature  increases,  this  maximum  is  less 
and  less  marked  until  it  eventually  vanishes,  as  in  the  case  of 
hydrogen.  The  following  table,  drawn  up  for  this  gas,  shows 
at  the  same  time  that  the  mean  coefficient  decreases  uniformly 
when  pressure  increases. 

HYDROGEN 


Pressure 

17°—  60° 

60°—  100° 

40  Meters 
100 
180 
260 
320 

.0033 
.0033 
.0031 
.0030 

.0028 

.0029 
.0028 
.0027 
.0025 
.0024 

I  may,  therefore,  summarize  the  laws  relative  to  the  expan- 
sion of  gases  in  the  following  way : 

1.  The  coefficient  of  expansion  of  gases  (referred  to  the  unit  of 
volume)  increases  with  pressure  up  to  a  maximum  value,  beyond 
which  it  decreases  indefinitely. 

2.  The  pressure  corresponding  to  this  maximum  coincides  in 
position  with  the  pressure  for  which  the  product  pv  is  a  minimum. 
Consequently,  at  this  exceptional  point  the  gas  accidentally  obey* 
the  law  of  Mariotte. 

38 


THE    LAWS    OF    GASES 

3.  For  continually  increasing  temperatures  the  maximum  in 
question  becomes  more  and  more  indistinct  and  finally  vanishes. 


COVOLUME — ATOMIC  VOLUME 

We  have  seen  that  for  hydrogen  the  curves  obtained  are 
nearly  straight  lines,  and  that  the  same  is  the  case  for  carbon 
dioxide  and  for  ethylene  throughout  a  considerable  part  of  the 
region  beyond  the  minimum  ordinate.  We  have  seen  further- 
more that  for  increasing  temperatures  the  curves  tend  more 
and  more  to  become  straight  lines  throughout  their  whole  ex- 
tent, thus  again  resembling  the  phenomenon  observed  with 
hydrogen  at  temperatures  above  that  of  the  atmosphere.  In 
this  case  the  curves  become 

(1)  pv  —  a  p  -j-  1). 

The  initial  ordinate  b  being  the  value  of  pv  at  the  limit — i.e.,  fora 
pressure  infinitely  small,  if  the  laws  which  we  have  adduced  are 
true  under  these  conditions.  This  indeed  is  a  question  which 
has  not  yet  been  sufficiently  studied  and  which  I  shall  shortly 
take  up  again.  We  shall  therefore  regard  our  inferences  limited 
as  to  pressures  to  an  interval  within  which  the  results  present  a 
sufficient  degree  of  certitude.  As  to  hydrogen,  I  have  already 
stated  that  for  pressures  less  than  100  atmospheres  the  line  still 
shows  a  slight  curvature  even  at  100°  0.  But  it  is  reasonable  to 
admit  that  this  curvature  will  quite  vanish  at  temperatures  taken 
high  enough,  and  that  the  line  will  become  straight — at  least, 
above  the  pressures  in  the  neighborhood  of  normal  pressure. 

The  equation  (1)  may  be  put  in  the  form 

(*)  P(r-a)=b, 

b  and  a  being  constants.  The  result  arrived  at  is  therefore 
this,  that  at  a  given  temperature  the  product  of  the  pressure 
and  the  volume  diminished  by  a  constant  quantity  does  not 
vary.  If  furthermore  the  relation  is  written 

(j^tf-l, 

it  appears  that  when  p  =  cn,  v  =  a.  That  is,  a  is  the  volume 
which  the  gas  eventually  takes  when  pressure  increases  indef- 
initely. This  may  be  rationally  interpreted  by  considering  a  as 
the  absolute  volume  of  the  matter  within  the  gas,  supposing 
that  the  molecules  will  ultimately  touch  each  other,  and  not  the 
molecules  only  but  the  atoms  which  make  up  those  molecules. 


MEMOIRS    ON 

Dupre  and  M.  Hirn  have  reached  a  similar  conclusion  with- 
in certain  limits  by  different  methods,  and  in  a  way  quite  un- 
like that  which  I  have  just  explained  ;  but  their  inferences 
would  lead  to  interpretations  which  are  at  variance  with  my  re- 
searches, taken  as  a  whole. 

In  fact  Dupre,  from  fundamental  formulae  in  the  mechanical 
theory  of  heat,  which  he  treats  in  his  work  (Dupre,  Theorie  me- 
canique  de  la  chaleur),  deduces  the  following  law  which  he  calls 
the  law  of  covolumes,  as  an  approximation  of  a  higher  order  of 
accuracy  than  the  law  of  Mariotte.  I  will  quote  it  verbatim: 

"At  constant  temperature  the  pressures  of  a  mass  of  gas  vary 
inversely,  as  the  volumes  diminished  throughout  ~by  a  small  con- 
stant quantity  c0u0.  This  is  to  be  called  the  covolume  wlien  the 
volume  u0  under  normal  conditions  is  the  unit  of  volume." 

For  nitrogen,  carbon  dioxide,  and  air  the  covolume  of  Dupre 
is  positive  ;  for  hydrogen  it  is  negative.  Seeking  a  verification 
of  this  law  by  aid  of  the  numerical  data  in  the  classical  research 
of  Regnault,  Dupre  found  that  this  was  feasible  for  hydrogen, 
as  may  well  be  anticipated  after  what  has  just  been  said  ;  but 
for  nitrogen,  and  above  all  for  carbon  dioxide,  the  verification 
leaves  much  to  be  desired.  It  could  not  be  otherwise,  since  the 
law  of  the  covolume  presupposes  that  the  curve  representing 
the  results  in  the  above  co-ordinates  is  straight.  This  condition 
is  not  realized  for  the  case  of  nitrogen,  nor  for  carbon  dioxide, 
unless  it  be  for  temperatures  and  under  pressures  for  which 
the  covolume  becomes  precisely  contrary  in  sign  to  that  deduced 
by  Dupre.  The  law  of  the  covolume  with  the  interpretation 
given  to  it  by  this  physicist  cannot  therefore  be  admitted. 

M.  Hirn  has  published  an  elaborate  research  *  on  the  same  sub- 
ject. Endeavoring  to  interpret  the  variations  from  the  law  of 
Mariotte,  he  points  out  that  even  if  the  molecules  of  a  gas  exert 
no  reciprocal  action  on  each  other  the  gas  cannot  rigorously 
obey  this  law,  since  the  variable  part  of  the  volume  is  not  the 
total  volume  of  the  gas,  but  rather  the  latter  diminished  by  the 
volume  of  the  atoms.  This  is  equivalent  to  admitting  the  quan- 
tity a  defined  above.  M.  Hirn  contends  that  it  is  merely  the 
variable  part  of  the  volume  which  ought  to  enter  into  the  ex- 
.  pression  of  Mariotte's  law,  a  conclusion  far  from  evident. 

For  the  case  in  which  one  may  not  neglect  the  interactions 

*  Hirn  :  Theorie  mecanique  de  la  clialeur,  t.  ii. 
40 


THE    LAWS    OF    GASES 

of  the  molecules,  M.  Him  introduces  an  internal  pressure  to 
be  added  algebraically  to  the  external  pressure,  and  the  general 
expression  of  the  law  for  constant  temperature  becomes 


p  and  p  being  the  internal  pressures  corresponding  to  the  vol- 
umes Fand  V.  For  hydrogen  p  and  p'  would  be  approxi- 
mately zero,  whence 

P  (  V—  a)  =  const., 

an  expression  which  M.  Him  verifies  by  aid  of  the  data  of 
Regnault. 

For  nitrogen  this  correction  of  volume  becomes  insufficient, 
and  does  not  even  retain  the  same  sign.  It  is  therefore  neces- 
sary, in  order  to  explain  the  variation  of  this  gas,  to  admit  an 
internal  pressure  of  marked  value.  Now  if  this  is  the  case 
with  nitrogen  for  pressures  less  than  20  atmospheres,  one  cannot 
assuredly  deny  that  it  must  also  be  the  case  for  hydrogen  when 
this  gas  is  reduced  to  the  three-hundredth  part  of  its  volume. 
But  for  pressures  as  large  as  430  atmospheres,  and  very  cer- 
tainly even  for  higher  pressures,  the  law  for  the  compressibility 
of  hydrogen  is  given  by  the  equation 

p  (  V—  a)  =const. 

as  rigorously  as  for  smaller  pressures.  The  internal  pressure 
is  therefore  zero.  Furthermore,  if  we  examine  the  data  rela- 
tive to  carbon  dioxide  and  ethylene,  we  again  observe  that  for 
temperatures  near  the  critical  point  a  large  part  of  the  curve 
becomes  straight.  This  takes  place  for  carbon  dioxide  at  35° 
from  100  to  430  atmospheres  ;  and  the  same  phenomenon  is 
observed  at  18°  C.  between  the  same  limits  of  pressure,  even 
though  the  body  is  now  a  liquid  —  i.e.,  has  been  subjected  to 
what  is  properly  termed  liquefaction.  Under  these  conditions 
the  compressibility  of  the  gas  is  thus  represented  by  the  relation 

p(  V—  a  )=  const., 

and  a  has  the  same  value  as  at  100°  C.,  and  higher  temperatures 
where  the  same  formula  represents  the  phenomenon  from  the 
lowest  pressures  upward.  Hence  one  may  argue  that  under 
circumstances  in  which  the  internal  pressure  ought  to  attain  a 
very  large  value  (at  35°  between  100  and  400  atmospheres),  this 
pressure  would  actually  vanish  from  the  equation;  whereas  it 
would  show  a  preponderating  influence  between  normal  press- 
ure and  100  atmospheres,  where  it  ought  itself  to  explain  the 
greater  part  of  the  variation  of  volume. 

*  41 


MEMOIRS    ON 

I  have  already  shown  that,  even  after  making  full  allowance 
for  the  atomic  volume,  the  occurrence  of  an  internal  pressure 
in  such  a  way  as  to  represent  a  mere  addition  to  the  external 
pressure  is  quite  insufficient  to  give  an  account  of  the  variations 
from  Mariotte's  law.  The  demonstration  was  on  that  occasion 
based  on  numerical  difference's  of  rather  small  value.  To-day, 
with  the  new  results  which  I  have  reached,  I  am  able  to  make 
this  fact  much  more  evident.  I  will  therefore  take  up  the 
demonstration  again  and  complete  it,  introducing  in  its  turn 
the  atomic  volume. 

Let  V  be  the  volume  of  the  gas  at  the  pressure  P  and  the 

temperature  T\   let  a  be  the  corresponding  atomic  volume; 

let  the  gas  be  compressed  as  far  as  pressure  P',  and  let  V  be 

the  new  volume  at  the  same  temperature.     Hence  one  obtains 

(P+p)(V-a)      ! 

lP'+p')(V'~a)  (1) 

p  and  p'  being  the  internal  pressures  for  the  volumes  Fand  V. 

Now  let  the  gas  be  heated  as  far  as  T'  degrees  and  let  Pl  be 
the  pressure  needed  to  keep  the  volume  at  V.  The  internal 
pressure,  if  it  depends  only  on  the  mean  distance  apart  of  the 
molecules,  will  again  be  p. 

Compress  the  gas  until  its  volume  has  diminished  to  V  and 
let  PI  be  the  pressure  needed  for  this  purpose.  The  internal 
pressure  will  again  be  p'  for  the  reason  specified.  Hence  we 
should  obtain  :  {Pj+p)(r_a) 

(/Y+/)(F'-a)- 
Equations  (1)  and  (2)  may  be  put  under  the  following  form  : 

P(V-a)  p'(V'-a)  -J»(F-q). 

'p'(V'-a)~  P'(V'-a) 

(&       ZiLEz^)  -  1  ,/»'(F'-a)  -p(F-a) 

'-  ' 


Put  p'(V'-a)-p(V-a)  () 

P'(V'-a) 

nd  y(F'-a)-XF-«) 

Pi(V'-a) 


rp 


The  relations  (3)  and  (4)  now  become  : 
P'(F'~)=1+^ 

P'(V~-a)=l  +  a'' 

42 


/< 

(    Tl  . 


THE    LAWS    OF    GASES 


Here  a  and  a'  are  the  variations  from  Mariotte's  law,  after 
the  correction  for  atomic  volume  has  been  applied  ;  in  other 
words,  the  discrepancy  of  the  law  : 

p  (  V  —  a)  =  const. 

Furthermore,  by  dividing  (5)  by  (6)  : 

' 


Hence  the  departure  from  the  law  P(V—  a)  =  const.  must  be 
in  the  inverse  ratio  of  the  corresponding  final  pressures  Pt 
and  P,'. 

As  an  example,  data  may  be  given  for  carbon  dioxide  at  35°.  4 
between  the  pressure  limits  30  and  70  atmospheres.  From  the 
isotherms  one  finds  at  once  that  at  pressures  of  40  and  220  at- 
mospheres at  100°  the  gas  has  the  same  volume  as  at  30  and  70 
atmospheres  at  35°. 

Hence  a  _220 

^"lo"' 

The  volumes  V  and  V  are  given  in  turn  by  the  ordinates 
corresponding  to  30  and  70  meters  of  mercury.  It  suffices  to 
divide  these  by  the  corresponding  pressures.  The  value  of  a 
is  deduced  from  the  straight  part  of  the  curves  of  which  it  is 
the  angular  coefficient.  Thus  without  difficulty 

F=7.9,   F'  =  1.03,  a  =  0.625. 
Hence  one  should  have 

(7.9-.  625)  30 


(1.03-.625)  70~~ 

(7.9-.  625)  40 

=  1  +  a  , 


(1.03-.625)220 
whence,  after  reduction, 

a  —5.65, 
a'=1.81. 
Finally,  in  accordance  with  equation  (7), 

5.65     220 

1^=40-  or  3.12  =  o.o, 

an  absurdity  out  of  all  proportion  with  such  discrepancies  as 
might  arise  out  of  mere  errors  of  experiment,  even  when  the 
approximate  method  of  verification  is  taken  into  account. 

The  so-called  internal  pressure  cannot  therefore  be  admitted 
into  gaseous  kinetics  in  so  far  as  this  pressure  is  to  depend  only 
on  the  mean  distance  apart  of  the  molecules — i.e.,  to  be  a 

43 


MEMOIRS    ON 

function  of  volume  only.  It  is  also  a  function  of  temperature, 
as  M.  Blaserna*  has  already  inferred  elsewhere. 

In  his  calculations  of  the  internal  work  of  a  gas  M.  Him 
makes  frequent  use  of  internal  pressure.  The  results  at  which 
he  thus  arrives  may  therefore  appear  discordant  with  my  own 
results.  Without  wishing  to  enter  into  a  detailed  discus- 
sion, I  will  remark  that  this  disagreement  can  onJy  be  appar- 
ent ;  it  is  due  simply  to  the  fact  that  rather  in  the  interior  of 
the  molecule  than  between  integrant  molecules  is  the  larger 
part  of  the  internal  work  expended.  It  does  not  follow  that 
the  values  of  internal  work  numerically  calculated  are  errone- 
ous. 

M.  Clausius  has  evolved  a  theory  which  has  since  become 
classic,  and  which  can  very  easily  give  an  account  of  the  dis- 
crepancies of  Mariotte's  law.  This  theory,  which  in  its  incep- 
tion is  traceable  to  Bernoulli,  and  the  first  kinetic  explana- 
tion of  Mariotte's  law  to  Kronig,  interprets  pressure  as  due  to 
the  impact  of  the  molecules  of  a  gas  on  the  walls  of  the  vessel 
holding  it.  Pressure  thus  depends  on  the  kinetic  energy  of 
the  translational  motion. 

When  a  gas  is  compressed  at  constant  temperature,  it  suffices 
to  assume  that  a  part  of  the  translational  or  intermolecular 
energy  is  transformed  into  intramolecular  energy  or  into  the 
energy  of  molecular  rotation,  to  give  a  complete  account  of 
the  discrepancy  of  Mariotte's  law.  For  the  result  would  be  a 
diminution  of  pv.  As  the  effect  of  atomic  volume  would 
make  the  law  deviate  in  a  contrary  sense,  one  is  led  to  antici- 
pate the  differing  phases  through  which  the  compressibility  of 
a  gas  passes,  according  as  one  or  the  other  of  the  two  causes 
supervenes.  It  is  even  possible  that  both  causes  may  annul  one 
another,  and  that  the  gas  thus  accidentally  obeys  Mariotte's 
law,  as  is  the  case,  for  instance,  in  the  region  of  minimum 
ordinates. 

Taken  as  a  whole,  the  results  which  I  have  reached  show 
pretty  clearly  that  a  special  theory  for  gases  and  another  for 
liquids  is  out  of  the  question.  Consider,  for  example,  the 
isotherms  of  hydrogen  :  how  is  it  possible  to  admit  one  theory 
to  explain  the  facts  represented  by  one  part  of  the  curves  and 
another  theory  to  explain  the  rest,  seeing  that  their  form  shows 

*  Blaserna  :  Comptes  rendus,  t.  Ixix.,  1869. 
44 


THE    LAWS    OF    GASES 

» 

conclusively  that  a  phenomenon  of  perfect  continuity  has  been 
observed  ?  Now  the  theory  of  impact  cannot  be  applied  to 
hydrogen  under  400  atmospheres,  since  under  these  conditions 
the  proximity  of  its  molecules  would  make  it  rather  a  liquid 
than  a  gas.  As  long  as  questions  on  the  condition  of  carbon 
dioxide  or  of  ethylene  at  ordinary  temperatures  are  upper- 
most, one  may  infer  that  the  two  parts  of  an  isotherm  situated  on 
each  side  of  the  minimum  ordinate  are  subject  to  the  different 
laws  ;  inasmuch  as  an  abrupt  variation,  which  may  reasonably 
be  interpreted  as  limiting  two  different  thermal  states,  sepa- 
rates them.  But  this  is  no  longer  applicable  when  the  gases 
are  subjected  to  higher  temperatures,  nor  for  hydrogen  (as  I 
have  stated)  even  at  ordinary  temperatures. 

It  is  very  remarkable  that  the  law  given  by  the  equation 
p(V—  a)  =  const.,  which  has  been  the  immediate  outcome  of 
my  experiments,  and  which  appears  to  be  the  limiting  law  tow- 
ards which  all  gases  converge  when  their  temperatures  are 
raised,  is  the  same  law  which  is  in  action  in  the  neighborhood 
of  the  critical  point,  whenever  the  compressibility  of  a  body  is 
considered  throughout  increasing  pressures.  Thus  it  is  rather 
a  law  for  the  liquid  than  for  the  gaseous  state.  I  will  even  add 
that  it  is  specifically  the  law  of  liquids — at  least,  within  the 
limits  of  actual  experimental  inquiry;  for  it  appears  from  the 
group  of  isothermals  that  carbon  dioxide  at  18°,  which  is 
then  truly  liquid,  follows  exactly  the  same  law.  Its  curve  is 
a  straight  line  whose  angular  coefficient  is  a.  Thus  we  arrive 
at  a  result  which  appears  at  first  sight  quite  paradoxical,  that 
elevation  of  temperature  transforms  the  gas  into  the  state  of 
a  perfect  liquid;  and  that  the  region  of  branches  of  the  iso- 
therms situated  on  the  left  of  the  line  of  minimum  ordinates, 
the  region  which  corresponds  accurately  to  the  gaseous  state 
in  the  ordinary  sense  of  the  word,  is  a  period  of  turbulence 
terminating  in  the  phenomenon  of  liquefaction  properly  so 
called.  This  phenomenon  disappears  when  temperature  rises 
indefinitely  and  the  body  becomes  a  perfect  fluid,  to  employ  a 
word  which  is  at  once  applicable  both  to  the  liquid  and  the 
gaseous  states. 

The  state  in  question  is  defined  by  the  simple  equation 
p  (  V—  a)  =  const.,  or  pW—  const.,  if  W  is  the  interatomic  vol- 
ume. The  law  thus  expressed  is  so  very  simple  that  one  is 
naturally  induced  to  seek  an  explanation  for  it  depending  sim- 

45 


MEMOIRS    ON 

ply  on  a  consideration  of  interatomic  volume ;  for  what  I  have 
already  said  about  internal  pressure  shows,  among  other  things, 
that  internal  pressure  does  not  appear  to  exert  as  much  in- 
fluence on  the  changes  of  volume  of  a  gas  or  of  a  liquid  as  has 
been  usually  supposed.  This  influence  should  be  reducible  to 
disturbances  quite  of  secondary  importance  in  their  bearing 
on  the  law  in  question — disturbances  which  may,  for  example, 
be  of  the  order  of  magnitude  of  the  discrepancies  of  Mariotte's 
law  occurring  within  the  limits  of  pressure  explored  by  Reg- 
nault. 

To  reach  an  explanation  based  purely  on  the  consideration 
of  atomic  volume,  let  us  observe  in  the  first  place  that  the  law 
PTF=const.  is  capable  of  the  following  enunciation  :  The  be- 
havior of  the  body  during  compression  is  such  as  if  an  infinite- 
ly subtle  fluid  rigorously  subject  to  the  law  of  Mariotte  per- 
vaded the  whole  space  between  the  molecules,  the  material 
particles  or  the  groups  which  they  form  showing  only  a  negli- 
gible amount  of  translational  kinetic  energy  and  producing  an 
effect  only  by  their  presence — i.e.,  by  the  volume  which  they 
delimit  i-n  the  same  way  as  if  they  were  ordinary  walls  of  the 
region. 

Why  may  not  this  fluid  be  the  ether  in  a  certain  degree  of 
concentration  ?  Such  an  hypothesis  would  give  a  complete 
account  of  all  observed  facts.  It  by  no  means  excludes  the 
theory  of  molecular  impact,  as  we  have  seen ;  it  merely  re- 
stricts the  limits  within  which  kinetic  action  is  applicable. 
Evidently  the  ether  ought  to  perform  some  function  relative 
to  the  phenomenon  with  which  we  have  been  occupied;  but 
this  role  has  never  been  specified,  nor,  so  far  as  I  know,  has 
anything  been  said  about  it.  If  one  considers  the  exclusive 
importance  of  the  ether  in  optic  phenomena,  the  relation  of 
these  to  thermal  phenomena,  and  the  close  connection  of  the 
latter  with  those  which  we  have  been  investigating,  the  strong 
probability  that  the  ether  must  fulfil  some  important  function 
is  manifest. 

It  seems  probable  that  the  molecules  are  surrounded  in  every 
thermal  state — solid,  liquid,  or  gaseous — with  atmospheres  of 
ether.  These  atmospheres  account  for  their  perfect  elasticity, 
as  evidenced  in  the  kinetic  theory  of  gases — an  elasticity  which 
it  would  be  very  difficult  to  explain,  or  which  would  be  even 
quite  inexplicable,  if  the  molecules  were  simple— i.e.,  reduced 

46 


THE    LAWS    OF    GASES 

to  single  atoms.  Granting  this,  let  a  gas  be  considered  at  low 
pressure  and  at  a  temperature  but  little  above  the  critical 
point.  Let  the  gas  be  compressed  at  an  initially  constant 
temperature.  The  theory  of  molecular  impact  deduces  Ma- 
riotte's  law  in  the  usual  way.  Changes  in  the  distribution  of 
kinetic  energy  between  the  motion  of  molecular  translation, 
the  motion  within  the  molecule,  and  its  rotational  motion 
suffice  to  explain  the  discrepancies  of  the  law,  to  which,  in  a 
certain  measure,  molecular  attraction  may  join  its  effects. 
Thus  the  gas  is  more  compressible  than  Mariotte's  law  indi- 
cates, even  if  allowance  be  made  for  the  absolute  volume  of  the 
atoms.  Very  soon,  however,  these  with  their  atmospheres  of 
ether  occupy  the  major  part  of  the  volume,  and  so  hamper 
each  other  in  their  movements  of  translation  that  the  latter 
virtually  vanish.  This  occurs  in  the  neighborhood  of  the  min- 
imum ordinate.  Finally,  for  continually  increasing  pressures 
the  atmospheres  of  ether  will  actually  become  contiguous,  and 
the  molecules  appear  as  if  suspended  therein.  The  ether  now 
forms  a  medium  which  is  continuous,  and  by  its  reaction  pro- 
duces the  observed  pressure  against  the  walls  of  the  vessel.  If 
this  ether  obeys  Mariotte's  law,  which  is  now  to  be  regarded  as 
the  limiting  law  of  an  infinitely  subtle  fluid,  the  volume  which 
it  occupies  is  exactly  W,  and  PPT^const.,  or  P  (V—  a)=const. 
Hence,  although  there  has  been  no  liquefaction  in  the  true 
sense  of  the  word,  the  body  is  rather  a  liquid  than  a  gas,  for 
the  reason  that  the  molecular  translational  motion,  which  is  a 
criterion  for  the  gaseous  state,  has  vanished. 

With  the  beginning  of  an  increase  of  temperature,  the  ethe- 
real molecular  atmospheres  will  expand  simultaneously  with 
the  molecules  themselves,  and  the  atoms  separate  more  and 
more  fully  until  decomposition  ensues.  Inasmuch  as  the  total 
volume  of  the  ethereal  atmospheres  is  larger,  the  law  p  W= 
const,  ought  to  begin  to  apply  for  a  given  mass  of  gas  at  a 
larger  volume  than  at  the  lower  initial  temperatures.  This 
indeed  appears  very  well  to  account  for  the  fact  that  for  a 
given  mass  of  gas  the  volume  corresponding  to  the  minimum 
ordinate  increases  with  temperature. 

If  temperature  continually  rises,  the  fraction  of  the  total 
volume  occupied  by  the  ether  also  continually  increases,  and 
when  the  effect  of  the  latter  preponderates  the  curves  will  rise 
and  be  gradually  transformed  into  straight  lines. 

47 


MEMOIRS    ON 

Perhaps  I  ought  to  add,  in  order  to  escape  an  unfavorable 
issue,  that  the  ether  taken  into  consideration  here  is  that  only 
which  is  retained  by  and  condensed  around  the  molecules  in 
the  form  of  a  molecular  atmosphere.  The  ether  which  is  not 
so  condensed  but  pervades  the  molecular  spaces,  whatever  be 
the  distance  apart  of  the  molecules,  is  without  relevant  in- 
fluence. This  does  not  oppose  any  reaction,  and  for  it  the 
walls  of  the  vessel  do  not  exist. 

The  hypothesis  which  I  have  just  formulated  thus  renders  a 
natural  and  complete  account  of  the  details  of  the  phenomena 
brought  out  by  experiment.  It  does  not  exclude  those  kinetic 
theories  which  have  gained  general  acceptance  among  physi- 
cists. So  far  as  I  can  see,  it  is  not  at  variance  with  any  estab- 
lished experimental  fact.  It  restricts  the  limits  within  which 
the  theory  of  impact  is  apparently  applicable  by  establishing 
a  transition  from  the  liquid  to  the  gaseous  state,  which  may  be 
passed  continuously  and  the  mechanism  of  which  is  easily  in- 
telligible. Finally,  it  introduces  no  difficulty  whatever  into 
the  phenomenon  of  liquefaction  properly  so  called. 

I  have  already  stated  that  the  law  PW—  const.,  which  ap- 
pears to  be  the  general  law  for  fluids,  is  applicable  to  liquid 
carbon  dioxide  below  the  critical  point,  as  is  evidenced  by  the 
straight  isotherm  for  18°  contained  in  the  family  of  curves. 
I  endeavored  to  verify  the  same  fact  with  several  liquids,  nota- 
bly writh  chlorhydric  ether,  for  which  I  published  the  compres- 
sibilities as  far  as  100°  and  37  atmospheres  several  years  ago.* 
The  law  was  reproduced  with  a  very  fair  approach  to  accuracy ; 
but  in  order  that  these  verifications  may  not  be  over-estimated,  it 
is  well  to  insert  the  following  remark:  If  the  liquid  were  quite 
incompressible  its  isotherm  would  necessarily  be  a  straight  line, 
for  the  ordinate  would  vary  proportionally  to  p,  v  being  con- 
stant. For  liquids  in  general,  therefore,  inasmuch  as  they  are 
nearly  incompressible,  their  curve  must  differ  exceedingly  lit- 
tle from  a  straight  line,  no  matter  what  may  be  the  true  law  of 
compressibility.  It  is  thus  impossible  to  derive  any  very  cer- 
tain inferences  from  the  behavior  of  the  greater  number  of 
liquids.  For  liquid  carbon  dioxide,  however,  the  case  is  alto- 
gether different,  and,  a  fortiori,  for  hydrogen  between  limits  of 
pressure  as  far  apart  as  those  within  which  I  have  operated. 

*  Annales  de  Chimie  et  de  Physique  (5),  t.  xi. ;  Memoirs  sur  la  Comprem- 
bilite  des  Liquides. 

48 


THE    LAWS    OF    GASES 

I  have  still  to  give  the  numerical  values  of  atomic  volume, 
having  calculated  it  for  hydrogen,  carbon  dioxide,  and  ethy- 
lene,  all  of  which  contain  the  straight  parts  of  the  isotherms 
clearly  defined  and  of  marked  extent.  In  computing  the  limit- 
ing directions  of  the  lines  for  the  other  gases,  one  is  liable  to 
make  a  considerable  error. 

To  obtain  a  it  is  adequate  to  establish  the  relation 

p(r-.)=p'(r'-a) 

between  two  pressure  values  sufficiently  far  apart  and  compre- 
hending a  part  of  the  curve  sensibly  straight.  Thus  the  value 
of  a  is  deduced  from  p,  p',  v,  v',  given  by  experiment.  Hence 
one  obtains  the  atomic  volume  of  the  mass  of  gas  subjected 
to  the  experiments  from  which  the  curves  were  constructed. 
This  mass  is  defined  by  the  normal  pressure  and  the  tempera- 
ture at  which  the  manometers  were  charged  with  gas. 

I  have  preferred  to  refer  the  atomic  volume  to  the  unit  of 
volume  of  the  gas  at  0°  C.  and  76  centimetres  of  mercury,  ob- 
taining the  following  values  : 

Hydrogen 0.00078 

Carbon  dioxide 0.00170 

Ethylene 0.00232 

Finally,  I  may  remark  that  the  interpretation  given  for  the 
value  of  a  is  independent  of  the  hypothesis  on  which  the 
theory  of  the  gaseous  state  is  founded.  It  will  readily  be  seen 
that  it  is  enough  that  the  curves  of  compressibility  should 
tend  to  become  straight  lines  in  the. limit;  for  under  these 
conditions 

pv  =  a  p  +  by  or  V—a  for  jo  — oo. 

No  matter  to  what  theory  one  may  subscribe,  therefore,  a  ap- 
pears as  the  smallest  absolute  volume  which  the  matter  can 
occupy.  One  naturally  infers  that  this  is  the  atomic  volume. 
This  remark  is  particularly  applicable  to  hydrogen,  the  iso- 
therms of  which  are  practically  straight  throughout  their 
whole  extent.  For  the  other  gases  the  determination  of  a  rests 
on  the  inferences  deduced  from  the  curves  as  a  whole,  but  less 
certainly.  The  results  are  therefore  given  with  less  assurance. 

To  pursue  this  subject  exhaustively  within  the  limits  which 
I  have  set  for  myself,  it  will  still  be  necessary  to  study  the 
compressibility  under  conditions  of  pressure  lower  than  those 


MEMOIRS    ON    THE    LAWS    OF   GASES 

occurring  in  the  present  research.  These  experiments  will  be 
made  directly  with  an  open  manometer.  I  hope  to  carry  the 
measurements  as  far  upward  as  300°.  I  hope  also  to  trace  the 
phenomena  further  into  the  region  of  extremely  low  pressures 
— a  few  millimetres,  for  instance — on  which  subject  1  have  al- 
ready published*  an  introductory  paper. 

Returning  again  to  these  experiments,,  I  shall  be  in  a  position 
to  add  many  material  improvements  to  the  method  which  I 
formerly  employed,  and  above  all  to  the  apparatus.  They  will 
be  completed,  I  hope,  in  the  course  of  the  next  academic  year. 

*  Annales  de  Ghimie  et  de  Physique,  t.  viii.,  1876 


MEMOIR    ON    THE    ELASTICITY    AND 

THEEMAL  EXPANSION  OF  FLUIDS 

THROUGHOUT  AN  INTERVAL 

TERMINATING   IN   VERY 

HIGH  PRESSURES 

BY 

E.  H.  AMAGAT 

(Anncdes  de  Chimie  et  de  Physique,  6°  Serie,  t.  xxix., 


CONTENTS 

PAGE 

PART  L— Method*  of  Manipulation : 

Introduction 53 

Methods  of  Experimentation  : 

1.  The  Measurement  of  High  Pressures — Manometre  d  Pis- 

tons Libre 55 

2.  Apparatus  for  Extremely  High  Pressures  : 

Method  of  Electrical  Contact 61 

Details  of  Manipulation 65 

Plan  of  a  Series  of  Measurements 67 

3.  Apparatus  for  Higher  Temperatures  : 

Method  of  Sights 71 

Preliminary  Operations 75 

PART  II— Data  for  Oases. 77 

Results  Obtained  by  tJie  First  Method  (Method  of  Electrical 

Contacts] 78 

Results  Obtained  by  the  Second  Method  (Method  of  Sights) . .  80 
Examination  of  the  Results  : 

General  Laws 89 

Coefficients  of  Expansion  at  Constant  Pressure  (-  —  j  . .     94 

Variation  of  the  Coefficient  of  Expansion  with  Press- 
ure , 97 

Variation  of  the   Coefficient  of  Expansion   with   Tem- 
perature      98 

Coefficients  of  Expansion  at  Constant  Volume  fi=(-  —  Y 

and  Pressure  Coefficients  B  =  — 101 

Variation  of  the  Coefficients  B  and  (3  with  Volume 104 

Variation  of  the  Coefficients  B  and  fi  with  Temperature.  104 


MEMOIR    ON    THE    ELASTICITY    AND 

THERMAL  EXPANSION  OF  FLUIDS 

THROUGHOUT  AN  INTERVAL 

TERMINATING    IN  VERY 

HIGH  PRESSURES 

BY 

E.  H.  AMAGAT 


PART  I. — METHODS  OF  MANIPULATION 
INTRODUCTION 

IN  the  Memoir  which  I  publish  to-day  I  have  brought  to- 
gether the  whole  of  my  researches  on  the  expansion  and  com- 
pressibility of  fluids,*  in  so  far  as  they  have  occupied  me  dur- 
ing the  last  ten  years.  A  part  only  of  the  results  has  been 
published  in  the  Comptes  Rendus  de  V Academic  des  Sciences; 
the  experimental  portions,  moreover,  were  sketched  with  the 
utmost  brevity  compatible  with  clearness. 

The  present  researches  for  gases  are  a  direct  continuation  of 
my  earlier  work  on  the  same  subject.  In  the  latter  the  limits 
of  pressure  and  of  temperature  employed  were  too  narrow,  and 
the  number  of  isotherms  mapped  out  not  great  enough  to  re- 
veal certain  relations  which  appear  very  clearly  in  the  present 
results.  Such  are,  for  example,  the  form  of  the  isotherms  in 
the  region  of  the  critical  point  which  lay  beyond  the  limits  of 
my  first  group  of  curves ;  furthermore,  the  contours  of  these 

*  The  parts  of  this  great  memoir  referring  to  liquids  will  not  be  in- 
cluded in  the  present  translation. 

53 


MEMOIRS    ON 

curves  in  the  region  lying  to  the  right  of  the  locus  of  minimum 
ordinates,  and  in  which  the  isotherms  under  very  great  press- 
ure seem  to  merge  into  straight  lines,  etc. 

As  for  liquids,  the  question  was  virtually  untouched  when 
these  researches  were  begun.  The  increase  of  the  coefficient 
of  compressibility  with  temperature  had  been  observed  for 
some  liquids,  together  with  the  contrary  effect  for  water.  I 
myself  extended  these  results,  in  a  memoir  published  in  1877, 
to  a  large  number  of  liquids,  and  within  limits  of  pressure  and 
of  temperature  beyond  any  which  had  been  applied  at  that  time ; 
but  the  laws  as  a  whole  were  yet  to  be  investigated,  the  deter- 
mination of  pressure  coefficients  was  not  even  attempted,  the 
data  relative  to  the  variation  of  the  coefficient  of  compressibil- 
ity with  pressure  were  altogether  contradictory.  Well-known 
treatises  of  physics  even  to-day  contain  errors  in  relation  to 
this  subject  which  surpass  the  limits  of  plausibility.  Since 
that  time,  however,  several  important  researches  bearing  on 
these  phenomena  have  been  published  outside  of  France. 

The  researches  which  I  am  about  to  describe  have  been  made 
with  a  view  towards  reaching  the  highest  attainable  pressures, 
both  for  liquids  and  for  gases.  It  is  my  purpose,  furthermore, 
to  make  special  investigations  for  the  low  pressures — i.e.,  for 
the  first  one  hundred  or  two  hundred  atmospheres,  and  there- 
after to  co-ordinate  them  in  such  a  manner  as  to  give  a  com- 
plete presentation  of  the  phenomena.  Experiments  devised 
to  reach  a  thousand  or  several  thousand  atmospheres  must  at 
lower  pressures  of  necessity  show  an  inferior  degree  of  accuracy 
than  may  be  reached  in  experiments  specially  adapted  to  the 
latter.  Circumstances  have  not  permitted  me  to  terminate 
this  research,  but  the  most  difficult  part  of  it  is  finished. 

In  this  place  I  may  be  permitted  to  say  that  the  instruments 
which  are  to  be  described,  as  well  as  all  others  used  in  my  re- 
searches for  upwards  of  fourteen  years  (1877  to  1891),  were  con- 
structed, in  the  workshop  attached  to  my  department  (service) 
at  Lyons,  by  M.  Gianotti  (at  present  instrument -maker  in 
Lyons).  My  tasks  have,  throughout,  been  singularly  facili- 
tated both  by  his  skill  in  construction  and  by  the  earnestness 
with  which  he  aided  me  in  the  experimental  work. 

Glass  apparatus  was  made  by  M.  Alvergniat,  or  by  his  suc- 
cessor, M.  Chabaud.  Indeed,  all  the  apparatus,  either  of  ordi- 
nary or  of  cut  glass,  which  has  been  used  in  my  experiments 

54 


THE    LAWS    OF    GASES 

for  twenty-five  years  or  more,  was  constructed  by  these  gentle- 
men. I  need  not  further  advert  to  their  services,  cheerfully 
rendered  in  the  cause  of  science. 

I  shall  first  describe  the  methods  and  the  apparatus.  They 
are  of  like  construction,  both  for  liquids  and  for  gases,  except 
as  to  the  piezometer  containing  the  fluid  and  the  manner  of 
charging  it.  I  shall  begin  with  the  apparatus  for  pressure 
measurement. 


METHODS   OF   EXPERIMENTATION 

The  Measurement  of  High  Pressures — "  Manometre  a  Pistons 

Litres." 

When  I  undertook  the  present  researches  there  was  no  in- 
strument available  for  the  accurate  measurement  of  pressure 
beyond  the  range  within  which  it  was  customary  to  compare 
the  well-known  empiric  pressure-gauges  with  the  open  ma- 
nometers. In  practice  closed  gas  manometers  are  subject  to 
serious  inconveniences.  Moreover,  they  cannot  be  employed 
above  420  atmospheres,  this  being  the  upper  limit  of  the  meas- 
urements which  I  made,  in  1878,  with  an  open  manometer  in 
the  shaft  of  the  mine  at  Verpilleux. 

The  principle  of  the  instrument  improperly  called  manometre 
de  Desgoffe*  solves  the  question  theoretically;  but  the  practical 
construction  adopted  was  actually  so  defective  that  no  reliance 
could  be  put  on  its  indications.  The  manometers  of  the  valve 
or  plug  type  may  perhaps  render  service  in  certain  cases.  M. 
Marcel  Deprez  has  improved  them  by  replacing — for  the  first 
time,  I  believe — the  valve  by  a  free  plunger  (piston  litre),  which 
does  not  allow  water  to  pass  except  with  extreme  slowness. 
But  these  instruments  even  when  perfected  are  not  available  in 
researches  which  cannot  well  be  conducted  without  a  pressure- 
gauge  of  continuous  registry. 

The  grave  difficulty  in  the  way  of  a  realization  of  Gaily - 
Cazalat's  idea  is  this  :  to  make  the  pistons  perfectly  free  to 
move  while  at  the  same  time  obviating  leakage.  For  the  large 
piston  the  difficulty  is  in  a  certain  measure  solved  by  the  ad- 

*  This  instrument  was  invented  by  Gally-Cazalat  ;  constructed  at  first 
by  Clair,  then  by  Bianchi,  and  finally  by  Desgoffe. 

55  y     v-          OF  THB 

UNIVERSITY 


MEMOIRS    ON 

dition  of  au  india-rubber  membrane.  Nevertheless,  this  in- 
genious device  is  not  quite  beyond  criticism ;  for  in  the  first 
place  the  sectional  surface  is  badly  determinate,  while  in  the 
second  the  action  of  the  membrane  gives  rise  to  an  error  which 
the  operator  must  either  endeavor  to  estimate  or  to  obviate. 
In  the  first  instruments  which  I  constructed  I  retained  the 
membrane  design,  but  an  index  rigidly  attached  to  the  large 
piston  enabled  me  to  follow  its  motion,  and,  therefore,  that  of 
the  membrane  also.  It  was  then  my  purpose  to  provide  the 
apparatus  with  a  regulating  pump,  which  by  injecting  a  vari- 
able quantity  of  liquid  below  the  membrane  would  enable  me 
to  keep  it  always  in  the  same  horizontal  plane,  thus  suppress- 
ing nearly  completely  the  action  referred  to.  Later  I  found  it 
more  advantageous  to  do  away  with  the  membrane  altogether 
and  to  leave  the  large  piston  entirely  free. 

To  secure  freedom  from  leakage,  I  found  it  sufficient  to  give 
the  piston  a  suitable  thickness  and  to  replace  the  actuating 
water  by  a  lubricating  and  at  the  same  time  slightly  viscous 
liquid ;  castor-oil  is  very  serviceable  for  this  purpose. 

The  analogous  difficulty  remained  for  the  case  of  the  small 
piston,  which,  experiencing  strong  pressure  in  a  leather-lined 
stuffing-box,  moved  only  with  difficulty  and  by  jerks.  It  was 
necessary  to  make  this  piston  free,  like  the  first,  but  the  con- 
dition of  no  leakage  was  here  very  much  more  difficult  of  at- 
tainment in  spite  of  the  small  section.  For  while  the  large 
piston  receives  only  the  relatively  small  pressure  of  the  counter- 
poising column  of  mercury,  the  enormous  total  pressure  which 
is  to  be  measured  bears  down  upon  the  small  piston.  I  suc- 
ceeded, however,  in  meeting  the  present  difficulty  by  the  identi- 
cal artifice — i.e.,  by  using  a  sufficiently  viscous  liquid,  in  this 
case  molasses.  Nevertheless,  the  function  of  this  body  is  some- 
what different  from  that  of  the  castor-oil :  for  while  the  oil  con- 
tinually lubricates  parts,  oozing  with  extreme  slowness  between 
them  in  a  way  not  to  interfere  with  effective  action,  the  mo- 
lasses penetrates  the  space  around  the  piston — supposed  to  be 
well  oiled  in  advance — with  very  great  difficulty  even  at  very  high 
pressures.  When  the  molasses  has  succeeded  in  penetrating 
and  removing  the  oil,  the  apparatus  still  functions,  although 
with  loss  of  same  of  its  original  sensitiveness.  It  is  then  pref- 
erable to  detach  the  small  piston  and  to  clean  it.  When  the 
apparatus  has  been  Adjusted  with  care,  it  is  sufficient  to  place 

56 


THE    LAWS    OF    GASES 

an  object  of  even  insignificant  weight  on  the  large  piston  to 
produce  a  corresponding  small  ascent  of  the  column  of  mer- 
cury. The  small  piston  is  in  general  less  sensitive,  above  all 
after  the  molasses  has  penetrated  between  it  and  the  socket. 
Finally  I  succeeded  in  quite  annulling  the  resistance  due  to 
friction  by  impressing  on  both  pistons  a  slight  movement  of 
rotation.  An  analogous  artifice  has  long  been  employed  by 


FIG.   1. — FREE-PISTON  MANOMETER  (Manometre  d  Pistons  Libres). 

M.  Bourdon  to  overcome  the  friction  of  the  piston  of  the  ap- 
paratus used  in  standardizing  his  spirals  ;  but  while  the  leather- 
lined  stuffing-box  requires  a  rapid  movement  of  rotation  in 
order  to  obviate  the  friction  of  a  tight  fit,  my  apparatus  needs 
only  a  slow  and  slight  angular  displacement  of  the  pistons  in 
order  that  the  column  of  mercury  may  at  once  take  its  definite 
position  of  equilibrium. 

Fig.  1  gives  a  section  of  the  apparatus.     The  liquid  trans- 
mitting pressure  arrives  by  the  tube,  c,  through  a  channel  in  the 

57 


MEMOIRS    ON 

piece  of  steel,  b,  screwed  to  the  brass  *  lid,  a.  This  piece  secures 
the  socket  of  tempered  steel,  d,  holding  it  down  free  from  leak- 
age by  aid  of  round  leather  washers.  The  small  piston,  also 
of  tempered  steel,  moves  up  and  down  in  this  socket.  The 
parts  are  so  fashioned  that  a  small  chamber,  00,  is  left  below 
b.  Into  this  the  charge  of  molasses  is  to  be  put.  The  lower 
end  of  the  small  piston  abuts  against  a  small  plane  of  tempered 
steel,  which  is  seen  in  the  figure,  screwed  to  the  centre  of  the 
large  piston,  P.  A  valve-screw,  d' ,  may  be  raised  to  admit  of 
the  escape  of  air  from  below  in  adjusting  the  apparatus.  Cir- 
cular grooves  are  cut  equatorially  around  the  outer  walls  of  the 
large  piston.  The  oil  accumulates  in  these  channels  during 
its  upward  leakage,  and  finally  reaches  the  hollow  part  or  cup 
of  the  large  piston.  The  latter  moves  up  and  down  in  a  mas- 
sive envelope,  also  of  brass.  This  is  screwed  down  to  a  heavy 
trough  of  cast-iron,  serving  as  the  base  of  the  apparatus,  by  a 
crown  of  square-headed  bolts,  and  further  secured  to  the  lid,  a, 
of  the  apparatus  by  a  second  crown  of  longer  bolts.  A  key, 
not  shown  in  the  figure,  may  be  attached  to  the  large  piston  at 
its  centre,  for  the  purpose  of  withdrawing  or  of  inserting  it. 
In  such  a  case  the  key  replaces  the  small  plane  of  steel. 

On  the  right  side  of  the  figure,  and  screwed  to  a  lateral  pro- 
jection of  the  trough,  is  the  steel  coupling  carrying  the  glass 
tube  in  which  the  mercury  column  rises.  This  coupling  con- 
sists of  two  parts :  the  lower  part  carries  a  stopcock,  and  thus 
the  operator  is  able  to  remove  the  glass  tube,  even  when  the 
trough  is  charged,  without  spilling  the  mercury  within  it.  At 
the  left  of  the  figure,  and  symmetrically  placed,  is  the  regu- 
lating pump,  and  this,  for  a  reason  similar  to  the  one  just  given, 
also  consists  of  separable  parts  with  a  stopcock  in  the  lower. 
The  channel  by  which  the  oil,  H,  is  injected  is  prolonged  by  a 
tubulure  extending  upward  much  above  the  mercury  surface, 
Jf,  in  order  that  this  may  under  no  condition  reach  the  pump, 
which  is  of  brass,  and  thus  in  danger  of  amalgamation. 

The  angular  movement  of  the  two  pistons  is  produced  by  the 
steel  rod,  mm',  screwed f  to  the  prolongation  of  the  small  pis- 

*  In  the  case  of  instruments  for  measuring  very  high  pressures,  the 
strength  of  the  brass  bolt  crown  is  insufficient  ;  the  central  part  of  the  lid, 
as  shown  by  the  dotted  lines,  should  be  made  of  steel. 

f  For  pistons  of  very  small  diameter,  this  prolongation  is  enlarged  and 
different  in  form. 

58 


THE    LAWS    OF    GASES 

ton.  This  rod  passes  between  two  pins,  i,  screwed  to  the  mar- 
gin of  the  large  piston,  arid  leaves  the  apparatus  through  a  win- 
dow in  the  upper  part  of  the  cylinder.  Thus  both  pistons  may 
be  put  into  the  same  horizontal  angular  motion,  which  is  trans- 
mitted by  a  simple  arrangement  not  shown  in  the  figure.  The 
regulating  pump  makes  it  possible  to  keep  the  stem,  mm',  at  a 
height  such  as  will  not  interfere  with  the  upper  or  lower  edge 
of  the  window.  Moreover,  by  an  inverted  action  of  the  appur- 
tenances of  the  manometer,  the  pump  maybe  made  to  produce 
very  considerable  pressures  above  the  small  piston  and  in  the 
space  where  the  bodies  subjected  to  experiment  are  placed ;  it 
is  often  convenient  to  make  use  of  this  method  to  regulate  the 
pressure  at  the  moment  of  measurement.  M.  Vieille  *  has  re- 
cently made  a  very  happy  application  of  this  artifice,  in  con- 
nection with  his  studies  on  the  behavior  of  the  crushing  ma- 
nometer (manometre-crusliers). 

If  well  constructed,  my  apparatus  will  give  pressure -values 
of  remarkable  uniformity,  the  accuracy  of  which  depends  only 
on  the  sectional  ratio  of  the  two  pistons.  The  sensitiveness 
can  be  increased  at  pleasure  by  increasing  the  value  of  this 
ratio  and  making  use  of  a  graded  series  of  pistons.  The  ap- 
paratus which  I  used  was  provided  with  two  large  pistons,  the 
one  6  centimetres  and  the  other  about  12  centimetres  in  di- 
ameter, together  with  a  series  of  small  pistons,  the  smallest 
being  5.527  millimetres  in  diameter. 

The  absolute  error  is  about  the  same  throughout  the  whole 
scale  of  pressures.  The  relative  error  would  become  intoler- 
ably large  if  a  few  atmospheres  only  were  to  be  measured, 
which,  however,  is  beyond  the  purposes  of  the  instrument.  It 
is,  nevertheless,  my  intention  to  construct  a  small  model  special- 
ly designed  for  the  lower  order  of  pressures,  and  I  hope  to  find 
it  relatively  quite  as  reliable. 

On  several  occasions  I  made  comparisons  of  data  for  the 
same  pressures  furnished  simultaneously  by  two  different  free- 
piston  manometers,  or  when  one  of  these  was  replaced  by  a 
closed  gas  manometer.  The  agreement  of  the  former  was  al- 
ways very  satisfactory,  but  this  was  usually  less  so  with  the  gas 
manometers.  I  do  not  hesitate  to  ascribe  these  discrepancies 
to  the  difficulty  of  manipulating  the  latter.  Here  is  the  com- 

*  Memorial  des  Poudres  et  Salpetres,  v. 


MEMOIRS    ON 

parison  of  the  free-piston  manometer  which  I  constructed  in 
1885  for  M.  Tait,  with  two  nitrogen  manometers  and  an  air 
manometer.  Pressures  are  given  in  atmospheres. 


TABLE   1. — MANOMETERS 


NITROGEN 

PISTON 

NITROGEN 

PISTON 

AIR 

PISTON 

226  Aim. 

224:  At  m. 

102  Atm. 

103  Atm. 

217  Atm. 

215  Atm. 

278  " 

275  " 

154  " 

154  " 

262  " 

263  " 

328  " 

326  " 

213  " 

215  " 

305  " 

306  " 

391  " 

387  " 

256  " 

257  " 

358  " 

362  " 

438  <{ 

438  " 

299  " 

297  " 

401  " 

406  " 

363  " 

359  " 

408  " 

402  " 

Never  did  the  comparisons  of  free-piston  manometers  present 
like  divergencies. 

The  following  table  contains  a  comparison  between  the  re- 
sults given  by  a  membrane  manometer  with  but  one  free  piston 
and  a  manometer  with  two  free  pistons  : 


TABLE  2. — MANOMETERS. 
MEMBRANE.  TWO  PISTONS.  RATIO. 

103  Atm..       ,  102  Atm. .         .  1.010 


156 
215 

260 
304 
368 
444 
550 
604 
697 


154 
213 

257 
301 
364 
439 
545 
600 
692 


1.013 
1.010 
1.012 
1.010 
1.011 
1.011 
1.009 
1.007 
1.007 


The  agreement  of  piston  and  gas  manometers  improves  when 
the  latter  are  used  under  the  best  conditions. 

In  Table  3  are  the  results  of  a  comparison  with  an  air  and  a 
nitrogen  manometer,  devised  for  very  high  pressures,  much 
more  sensitive  than  the  above,  and  directly  graduated  for  each 
gas  by  comparison  with  a  column  of  mercury  in  one  of  the 


THE    LAWS    OF    GASES 

towers  of  the  Fourviere  cathedral  in  Lyons — that  is,  under  the 
best  conditions  possible.  The  free-piston  manometer  was  it- 
self so  adjusted  that  fractions  of  an  atmosphere  were  easily  read 
off. 

TABLE  3.— MANOMETERS 


AIR 

PISTONS 

NITROGEN 

PISTONS 

OPEN 
MANOMETER 

PISTONS 

•20.36  Atm. 

26.32  Atm. 

26.29  Atm. 

26.50  Atm. 

1.66  Atm. 

1.74  Atm. 

32,39     " 

32.34     " 

32,51     " 

33.59     " 

2.95     " 

3.02     " 

38.34     " 

38.44     " 

39.12      ' 

39.21     " 

5.07     " 

5.16     " 

44.98     " 

45.00     " 

45.77      ' 

45.81     " 

6.52     " 

6.61     " 

50.92     " 

51.05     " 

52.26      ' 

52.41     " 

57.37     " 

57.50     " 

58.12       ' 

58.87     " 

64.24     " 

64.16-   " 

65.35       < 

65.53     " 

72,15     " 

72,45     " 

71.00     " 

71.36     " 

Finally,  in  the  last  two  columns,  the  table  contains  a  com- 
parison, throughout  a  few  atmospheres  only,  with  an  open 
mercury  manometer,  the  errors  of  which  may  be  regarded 
practically  zero.  The  discrepancy  is  obviously  inadmissible  for 
pressures  as  small  as  these ;  but  for  higher  pressures,  50  or 
60  atmospheres  for  example,  the  absolute  error  not  becoming 
larger,  the  results  are  exceedingly  satisfactory. 

For  the  series  of  measurements  reading  upward  as  far  as 
3000  atmospheres,  I  chose  a  pair  of  pistons  such  that  one  at- 
mosphere was  equivalent  to  1.601  millimetres  of  mercury  at 
0°  C.  For  the  series  limited  by  1000  atmospheres,  the  equiva- 
lent height  was  4.99  millimetres.  In  each  case  I  selected  those 
sectional  ratios  which  gave  me  the  highest  attainable  sensitive- 
ness for  the  case  of  a  column  of  mercury  5.20  metres  in  height, 
the  maximum  elevation  at  my  disposal. 


2.    APPARATUS    FOR   EXTREMELY    HIGH    PRESSURES 

Method  of  Electrical  Contact. 

The  methods  of  which  I  made  use  in  my  preceding  re- 
searches do  not  admit  of  being  carried  much  above  400  atmos- 
pheres. It  is  very  difficult  to  obtain  glass  tubes  which  will 
resist  interior  pressures  more  intense  than  this.  To  solve 
this  difficulty  by  plunging  the  piezometer  bodily  into  a  stronger 

61 


MEMOIRS    ON 

cylinder,  necessarily  metallic  and  opaque,  presents  grave  diffi- 
culties in  regard  to  the  reading  of  volumes.  Otherwise  it  is 
the  method  of  Oersted.  The  difficulty  in  question  was  first 
avoided  by  means  of  gravitational  apparatus,  or  by  covering  the 
interior  of  the  stem  of  the  piezometer  by  a  film  which  is  dis- 
solved by  the  liquid  transmitting  the  pressure,  thus  indicating 
the  height  to  which  it  has  been  raised.  These  procedures  have 
two  serious  defects  :  aside  from  the  fact  that  they  merely  give 
the  maximum  of  the  height  to  which  the  liquid  has  been  raised, 
they  are  quite  impracticable  for  the  construction  of  a  regu- 
lar series.  They  have  given  rise  to  very  grave  errors.  The 
method  pursued  for  gases  by  Natterer,  which  consisted  in  com- 
pressing a  known  volume  of  gas  into  a  given  space,  repeating 
the  operation  a  great  number  of  times  and  determining  the 
pressure  corresponding  to  each  accession,  is  certain  to  be  sur- 
rounded with  great  difficulties,  and  rapidly  becomes  quite  im- 
practicable if  one  endeavors  to  raise  the  temperature.  The 
work  of  Natterer  is  none  the  less  extremely  remarkable,  par- 
ticularly if  the  time  when  it  was  done  (1851)  is  called  to  mind. 
It  is  hard  to  explain  why  it  has  remained  so  long  unknown  in 
France. 

At  the  time  when  I  began  these  researches — that  is,  about 
1882 — M.  Tait  was  engaged  with  a  study  of  the  compressibility 
of  water,  and  he  called  my  attention  to  the  method  of  electric 
contacts  which  he  employed  in  his  researches.  Among  other 
things,  I  had  also  thought  of  this  artifice,  but  I  had  as  yet 
made  no  trial  of  it.  Upon  the  recommendation  of  the  eminent 
physicist  I  tried  it  at  once ;  and  since  then  I  have  employed  no 
other  method,  either  for  liquids  or  for  gases,  in  all  series  of 
measurements  carried  to  the  highest  attainable  pressures  and 
at  temperatures  not  exceeding  50°. 

Fig.  2  gives  a  sectional  elevation  of  the  apparatus  construct- 
ed for  these  researches.  The  receiver,  or  barrel,  GG,  in  which 
the  piezometer  is  placed  is  a  cylinder  of  steel  3  centimetres 
in  diameter  internally,  and  surrounded  by  a  steel  jacket,  G'G', 
to  a  point  about  as  far  down  as  the  bottom  of  the  aperture 
within.  The  total  outer  diameter  is  18  centimetres,  the  avail- 
able depth  of  the  receptacle  below  the  position  of  the  upper 
junction  is  about  88  centimetres.  The  somewhat  excessive  pro- 
longation of  the  unjacketed  breech  has  a  special  purpose  to 
which  I  shall  refer  below.  Pressure  is  transmitted  by  a  charge 


THE    LAWS    O 


ES 


of  water  injected  by  a  force-pump,  and  enters  at  D  by  way  of 
the  valve-coupling,  i?,  screwed  to  the  upper  part  of  .^fcne  receiver 
on  the  right.  When  the  pressure  attains  a  certain  value  de- 


FIG.  3. 


\  J 


FIG.  2. 

FIG.  2. — PRESSURE  APPARATUS  WITH  ELECTRICAL  CONTACTS. 
FIG.  3. — PIEZOMETER  FOR  GASES. 
FIG.  4. — PIEZOMETER  FOR  LIQUIDS. 
63 


FIG.  4. 


MEMOIRS    ON 

pending  on  the  upper  limit  which  is  to  be  reached,  the  screw- 
valve  is  closed,  and  compression  is  thereafter  continued  with 
the  use  of  the  device  screwed  to  the  head  of  the  receiver.  The 
central  piece,  A,  is  pierced  by  an  aperture  16  millimetres  in 
diameter,  in  which  a  cap-shaped  leather  washer,  C  (drawn  in 
larger  scale  at  the  side),  moves  up  arid  down.  This  washer  has 
the  form  of  a  little  cylinder  with  a  flat  base.  It  is  pushed  for- 
ward by  a  rod  of  steel,  P,  advancing  with  slight  friction  and 
terminating  in  a  cone  at  its  upper  end.  Here  the  motion  is 
impressed  upon  it  by  a  steel  screw,  F,  the  threads  of  which  are 
2  millimetres  apart  and  move  in  a  nut  of  brass  carried  by  a 
second  hollow  cylinder  of  steel,  B,  surrounding  the  central 
piece,  A.  This  second  cylinder  is  screwed  to  the  jacketed  re- 
ceiver, against  which  it  presses  the  central  piece,  A,  making  a 
pressure-tight  joint  with  it  by  the  aid  of  a  leather  washer. 
The  screw  is  actuated  by  a  four -armed  lever  seen  at  the 
top  of  the  apparatus.  At  the  left,  on  the  same  level  with  the 
influx  valve,  there  is  a  special  attachment,  F,  of  steel,  adapted 
to  carry  the  electric  current  into  the  piezometer,  insulated  from 
the  body  of  the  apparatus.  This  is  attained  by  aid  of  a  small 
cone  of  steel,  K,  preliminarily  inserted  into  the  channel  within 
the  piece,  F,  and  which  is  wedged  after  having  been  surround- 
ed by  a  very  thin,  small  conical  shell  of  ivory,  00,  insulating 
perfectly.  Moreover,  the  taper  of  the  cone  is  so  directed  that 
the  internal  pressure  will  force  it  into  more  intimate  contact 
with  its  surroundings.  The  small  steel  cone  joins  the  ends  of 
the  conducting  wires,  which  are  screwed  into  it  in  the  manner 
detailed  in  the  enlarged  figure.  This  attachment  has  never 
shown  the  least  trace  of  leakage. 

On  a  level  with  the  influx  valve  and  the  attachment,  F,  there 
is  still  a  third  coupling,  not  shown  in  the  figure,  which  puts  the 
barrel  in  connection  with  the  manometer  (these  three  pieces 
are  in  reality  placed  so  as  to  divide  the  circumference  of  the 
cylinder  into  three  equal  parts).  The  connecting  tube  is  about 
2  meters  long  and  made  up  of  three  parts  bored  at  the  lathe, 
the  last  piece  being  afterwards  bent  down  by  forging.  I  at  first 
employed  thick  tubes  of  drawn  steel,  but  they  burst  at  about 
2000  atmospheres. 

The  piezometer  containing  the  fluid  to  be  compressed  is  of  a 
form  shown  separately  in  Fig.  3  for  gases  and  in  Fig.  4  for  liq- 
uids. The  stern  carries  a  series  of  fine  platinum  wires  laterally 

64 


THE    LAWS    OF    GASES 

inserted  into  the  glass  and  reaching  as  far  as  the  middle  of 
the  bore.  Between  each  thread  there  is  inserted  an  electric 
resistance  wrapped  around  the  tube.  These  resistances  are 
made  up  of  wire  covered  with  india-rubber,  and  a  small  part  of 
each  coil  is  exposed  so  as  to  be  soldered  to  the  corresponding- 
ends  of  the  platinum  wires.  The  whole  is  then  covered  by  a 
wrapper,  insulating  perfectly  even  when  plunged  in  mercury, 
and  remaining  sufficiently  soft  to  insure  an  equal  compression 
of  the  glass  on  opposite  faces.  When  the  piezometer  is  placed 
within  the  barrel,  the  upper  terminal  is  joined  to  the  prolonga- 
tion seen  within  the  cone  of  the  attachment,  F,  contact  being 
thus  completed  throughout.  When  the  mercury  into  which 
the  lower  end  of  the  piezometer  is  plunged  rises  in  the  tube 
conformably  with  the  increasing  pressure,  and  just  touches  the 
first  of  the  lateral  platinum  wires,  the  current  may  be  closed 
between  any  part  of  the  barrel  or  its  metallic  appurtenances 
and  the  conductor  joined  at  the  outer  end  of  F. 

The  jacketed  part  of  the  barrel  is  further  enveloped  by  a 
spacious  brass  cylinder  filled  with  ice  or  charged  with  water 
kept  in  circulation  and  issuing  from  special  auxiliary  apparatus 
adapted  to  secure  constancy  of  temperature  between  0°  and 
about  50°  0.  Entering  near  the  bottom,  the  circulating  water 
issues  from  a  tubulure  near  the  top.  A  thermometer  shows  its 
temperature.  Two  stopcocks,  seen  at  the  bottom  of  the  water- 
jacket,  facilitate  influx.  The  bath  is  surrounded  with  wood 
sawdust,  contained  between  the  four  braced  timbers  of  oak, 
and  kept  in  place  by  shutters  not  shown  in  the  figure.  The 
upper  part  is  protected  with  felting. 

Details  of  Manipulation. — Let  the  case  of  a  liquid  be  first 
considered.  The  piezometer,  Fig.  4,  clean  and  dry,  is  filled 
with  the  liquid,  which  must  have  been  boiled  to  remove  the  air 
in  the  usual  way.  This  done,  a  column  of  mercury  several  centi- 
metres high  is  introduced  at  the  lower  end  of  the  stern  by  aid 
of  a  funnel,  the  end  of  which  has  been  drawn  out  to  as  long 
and  fine  a  point  as  desirable.  This  end  of  the  stem  is  then 
plunged  into  a  small  glass  full  of  mercury,  and  the  body  of  the 
piezometer  carefully  heated  until  the  meniscus  reaches  the 
lower  end.  On  cooling  the  mercury  again  rises,  and  the 
column  so  formed  is  very  uniform  and  free  from  breaks  due 
to  the  other  liquid.  Thereafter  the  stem  is  provided  with  a 
small  cylindrical  reservoir  of  steel,  and  the  stem  dips  into  the 
E  65 


MEMOIRS    ON 

mercury  contained  as  shown  in  the  figure.  It  is  now  neces- 
sary to  find  the  mass  of  the  liquid  operated  on.  For  this  pur- 
pose the  piezometer  is  submerged  in  a  long  test-tube  of  glass 
containing  mercury  at  its  lower  end,  into  which  the  little  steel 
reservoir  is  plunged.  A  current  of  water  at  constant  tempera- 
ture is  made  to  circulate  in  the  test-tube,  and  when  a  state 
of  thermal  equilibrium  has  been  reached  the  volume  of  the 
liquid  is  read  off  on  a  standardized  scale  etched  into  the  lower 
part  of  the  stem.  The  piezometer  may  now  be  put  into  the 
barrel  of  the  pressure  apparatus,  also  charged  at  its  bottom 
with  a  sufficient  quantity  of  mercury.  The  electric  circuit  is 
then  completed,  a  spring-stop  added  to  hold  the  piezometer  in 
place,  the  attachments  for  the  production  of  pressure  screwed 
on,  and  all  is  now  ready  for  making  a  series  of  measurements. 

In  the  case  of  gases,  the  following  operations  are  necessary: 
The  current  of  gas  is  passed  into  the  piezometer,  perfectly  dry, 
and  heated  from  time  to  time  during  the  operation,  and  passed 
out  through  the  fine  point  at  the  top.  At  suitable  periods  a 
sample  of  the  gas  is  tested,  and  when  the  examination  shows 
that  the  piezometer  contains  perfectly  pure  gas  only,  the  point 
at  the  top  is  closed  with  the  blow-pipe.  Thereafter,  without 
separating  the  piezometer  from  the  purifying  and  drying  train 
in  which  a  small  excess  of  pressure  is  kept  in  action,  the  pie- 
zometer is  received  and  held  vertically  by  a  tube  of  brass  in  a 
special  apparatus,  which  in  turn  is  submerged  in  a  glass  trough 
supplied  with  a  current  of  circulating  water.  When  the  tem- 
perature has  become  stationary,  the  normal  pressure  is  again 
established  in  the  dissicating  trains,  and  the  rubber  tube  con- 
necting this  apparatus  with  the  lower  end  of  the  piezometer, 
which  alone  is  outside  of  the  bath,  is  removed  with  caution. 
At  the  same  time  this  end  is  plunged  into  a  cistern  of  mer- 
cury. This  operation  to  be  well  made  requires  some  skill  and 
practice.  It  is  now  only  necessary  to  fit  the  small  steel  thimble 
to  the  lower  end  under  mercury,  and  to  place  the  piezometer 
in  the  barrel.  All  heating  which  may  cause  the  gas  to  flow 
out  during  the  adjustment  is  to  be  scrupulously  avoided.  It 
is  obvious  that  the  pressure  of  the  barometer  was  taken  at 
the  required  time,  and  that  the  mass  of  gas  is  thus  perfectly 
determinate. 

All  piezometers,  whether  adapted  for  liquids  or  for  gases,  were 
calibrated  with  mercury  in  such  a  way  that  the  instant  at  which 


THE    LAWS    OF    GASES 

the  mercury  touches  one  of  the  lateral  platinum  filaments  of 
the  tube  is  shown  electrically  precisely  in  the  manner  to  be 
adopted  during  the  experiments.  The  volumes  given  by  the 
calibration  tables  are  therefore  quite  identical  with  the  corre- 
sponding measurements  under  pressure. 

For  the  gas  piezometers,  in  particular,  this  standardization  is 
a  rather  delicate  operation  because  of  the  small  volumes  to  be 
measured.  I  carried  it  out  in  two  ways,  directly  in  weight  and 
indirectly  in  volume.  By  aid  of  a  standard  tube  calibrated  with 
great  care  and  temporarily  soldered  to  the  stem  carrying  the 
platinum  contacts,  I  measured  the  volume  of  mercury  which 
is  withdrawn  from  this  stem  while  the  column  is  made  to  glide 
from  one  contact  to'the  next.  In  this  case  the- small  olive- 
shaped  reservoir  just  below  the  upper  point  is  calibrated  sepa- 
rately. The  point,  though  very  fine,  is  itself  calibrated  from 
a  fiducial  mark  onward,  in  order  that  the  diminution  of  volume 
produced  when  the  fine  point  is  cut  off  and  resoldered  may  be 
estimated,  however  small  it  may  be. 

Plan  of  a  Series  of  Measurements 

Fig.  5  shows  the  completed  apparatus  and  its  accessories. 
In  the  rear  of  the  figure  is  the  tank  containing  the  water  to  be 
heated.  Constancy  of  temperature  is  obtained  by  the  aid  of  a 
crown  burner  of  gas,  a  regulator,  an  influx  tap,  and  an  over- 
flow, all  conveniently  disposed.  For  the  lower  temperatures, 
water  cooled  down  as  far  as  zero  in  a  refrigerator  is  raised  to 
any  desired  degree  of  temperature  by  its  passage  through  longer 
or  shorter  spirals  kept  within  appropriate  temperature  baths. 
On  the  left  is  seen  the  large  force-pump  communicating  with 
the  corresponding  stopcock  and  coupling.  Quite  in  front  is 
the  free-piston  manometer  with  the  lower  end  of  the  mercury 
column.  At  the  right,  on  a  bracket,  is  the  galvanometer,  in- 
serted into  the  electric  circuit  to  announce  the  galvanic  con- 
tacts. It  is  seen  at  once  how  the  first  instant  of  contact  is 
obtained.  For  the  others  I  adopted  the  following  arrange- 
ment :  The  current  is  branched  and  the  galvanometer  mounted 
differentially.  One  of  the  shunts  passes  through  the  resistances 
of  the  piezometer,  a  box  of  resistances,  and  a  rheostat.  The 
galvanometer  is  put  back  to  zero  after  each  contact,  and  these 
are  unmistakably  indicated  by  the  suppression  of  a  definite 
quantity  of  piezometer  resistance  whenever  the  contact  is 

67 


MEMOIRS    ON 

made.     The  force-pump  is  first  to  be  actuated  in  order  to 
completely  fill  the  apparatus  and  to  start  the  excess  of  internal 


FIG.  5. — DISPOSITION  OF  APPARATUS  FOR  VKRY  HIGH  PUKSSUUKS 

pressure.     To  find  the  exact   instant  of  contact  use  is  made 
of  the  compressing  screw,,  which,  moreover,  is  employed  ex- 

68 


THE    LAWS    OF    GASES 

clusively  as  soon  as  the  pressures  reach  values  of  400  to  500 
atmospheres. 

When  a  contact  is  obtained  it  is  necessary  that  the  apparatus 
should  return  again  to  its  initial  temperature,  since  this  has 
been  changed  by  the  thermal  effect  of  compression.  The 
initial  conditions  may  be  considered  as  established  when,  on 
breaking  and  reproducing  the  contact  many  times  by  means  of 
small  pressure  increments  slowly  applied,  it  is  found  to  recur 
uniform! vat  the  same  pressure.  This  pressure  is  then  marked 
with  a  fine  chalk  pencil  on  the  scale  of  the  mercurial  column. 
The  galvanometer  is  now  set  back  to  zero,  while  the  compres- 
sion is  continued  as  far  as  the  next  contact,  progressing  in  like 
manner  until  the  last  contact  is  reached.  Thereafter  the  series 
is  repeated  throughout  in  the  opposite  direction — i.e.,  all  con- 
tacts are  passed  again  in  a  march  of  decreasing  pressures. 

If  the  series  has  been  carried  to  completion  rather  too  rapid- 
ly, it  will  happen,  owing  to  the  inverse  thermal  effects  during 
the  periods  of  increasing  and  decreasing  pressures,  that  the 
pressures  observed  in  descending  will  be  a  little  smaller,  caet. 
par.,  than  those  observed  in  ascending.  The  difference  is 
usually  very  small,  and  the  mean  may  be  taken.  Its  value  at 
the  same  time  is  a  criterion  of  the  degree  of  accuracy  guaran- 
teed. 

When  the  constancy  of  temperature  in  the  apparatus  has 
been  exceptionally  good,  and  if  the  observer  has  waited  long 
enough  at  each  contact,  the  pressures  in  the  ascending  series 
are  exactly  reproduced  by  the  corresponding  pressures  in  the 
descending  series.  This  is  the  best  proof  which  can  be  given 
of  the  trustworthiness  of  the  instrument  used  in  measuring 
pressures. 

Work  may  be  done  more  expeditiously  by  completely  sub- 
merging the  piezometer  in  mercury.  The  thermal  effect  of 
compression  is  then  small,  and  by  reason  of  the  good  condition 
of  mercury,  the  thermal  equilibrium  is  re-established  very 
quickly.  In  this  case,  however,  the  insulation  of  the  resist- 
ances requires  much  greater  care. 

When  the  cylinder  and  the  piezometer  are  filled  with  water 
it  is  perfectly  feasible  to  put  in  evidence  the  reversal  of  the 
thermal  effect  of  compression  on  the  respective  sides  of  the 
temperature  of  maximum  density  of  water. 

These  operations,  which  require  the  concerted  observation  of 


MEMOIRS    ON 

at  least  three  persons,  are  long  and  tedious.  A  single  series 
may  extend  over  two,  three,  four  hours,  or  even  more,  depend- 
ing on  the  number  of  contacts  and  supposing  that  no  accident 
occurs. 

I  stated  above  that  the  prolongation  of  the  unjacketed 
breech  of  the  steel  cylinder  seemed  to  be  of  excessive  length. 
The  reason  of  this  design  may  be  found  in  an  accident  which 
happened  to  me  in  the  experiments  in  which  oxygen  was  com- 
pressed as  far  as  a  maximum  density  above  1.25  (relative  to 
water)  at  the  temperature  of  17°  C.  The  cylinder  was  quite 
strong  and  filled  with  mercury.*  Suddenly,  with  a  strident 
noise,  a  jet  of  pulverulent  mercury  was  hurled  across  the  right 
section  of  the  breech,  striking  the  base  of  the  apparatus,  re- 
bounding thence  to  more  than  a  metre  in  height  in  all  direc- 
tions. The  noise  was  like  that  produced  by  a  jet  of  steam 

•  escaping  from  a  boiler  under  high  pressure.     A  right  section 

•  of  the  column  after  being  polished  showed  nothing  in  particu- 
lar when  examined  under  the  microscope.     "We  have  thus  en- 
countered the  classical  experiment  of   the   rain  of   mercury 
through  the  pores  of  a  body  of  steel  about  .08  metre  thick. 
The  pressure  was  certainly  as  high  as  4000  atmospheres.     The 
same  apparatus  under  the  same  pressure  did  not  admit  of  the 
exudation  of  a  single  drop  of  glycerine.     It  would  doubtless 
have  shown  the  same  negative  result  for  water  and  for  other 
liquids. 

J^o  similar  accident  occurred  during  the  course  of  my  work, 
so  far  as  a  flow  normal  to  the  section  of  the  cylinders  used  is 
concerned.  The  reason  why  the  thickness  of  the  breech  was 
increased  to  an  extreme  degree  in  the  direction  of  the  axis  is, 
therefore,  clear. 

I  was  induced  to  devise  a  jacketed  cylinder  in  consequence 
of  an  accident  of  another  kind.  The  first  large  cylinder  of 
steel  which  I  used  (weighing  116  kg.)  split  apart  along  opposite 
generatrices  throughout  a  considerable  part  of  its  length.  Al- 
though there  was  neither  projection  nor  separation  of  parts, 
nor  any  sudden  issue  of  gas,  the  rupture  was  nevertheless  ac- 
companied with  a  detonation  of  extreme  violence.  During  a 
few  moments  the  mercury  escaped  from  the  fissure,  and  I  bad 
time  to  observe  it  in  form  of  .a  bright  metallic  plate  6  to  7  cen- 

*-Cvmpt€8  RendiiH.  March  2,  1885. 
70 


THE    LAWS    OF    GASES 

timetres  in  breadth.  It  was  owing  to  the  occurrence  of  these 
two  accidents  that  I  added  the  steel  jacket  to  the  cylinder,  as 
already  described. 


3. — APPARATUS  FOR  HIGHER  TEMPERATURES 

Method  of  Sights. 

It  would  be  difficult  to  work  at  temperatures  markedly  higher 
than  those  for  which  the  apparatus  just  described  was  designed. 
The  mass  of  the  jacketed  steel  barrel,  the  presence  of  the  ap- 
pliances added  at  its  top  and  which  project  outside  of  the  bath, 
would  make  a  uniform  degree  of  high  temperature  very  diffi- 
cult of  attainment.  The  joints  and  the  cap-shaped  washer 
would  no  longer  insure  freedom  from  leakage.  Finally  and 
particularly,  for  the  case  of  gases,  the  piezometer  stems,  fragile 
at  best  by  reason  of  the  inserted  platinum  filaments,  would  be- 
come prohibitively  so,  while  the  difficulties  of  an  adequate  in- 
sulation of  the  parts  would  in  like  measure  greatly  increase. 

The  following  design,  which  I  shall  call  the  method  of  sights 
(methode  des  regards),  has  enabled  me  to  work  as  far  as  360°  C. 
It  would  even  be  possible  to  reach  higher  temperatures,  in 
modifying  the  apparatus  in  the  way  which  experience  has 
suggested,  but  which  I  do  not  expect  to  apply  at  present.  I 
have  also  thought  it  desirable  to  restrict  the  pressures  within 
1000  atmospheres,  although  in  many  trials  I  went  much  beyond 
this. 

The  method  may  expediently  be  described  together  with  the 
apparatus.  The  latter  is  represented  in  sectional  elevation  in 
Fig.  6.  In  the  lower  part  of  the  apparatus  the  jacketed 
barrel,  HH,  of  the  preceding  compressor  will  be  recognized, 
although  three  breaks  were  needed  to  shorten  the  figure.  At 
the  top  of  this  is  fixed  (as  above)  the  apparatus  for  producing 
pressure,  modified  by  the  introduction  of  a  cross  of  steel, 
A,  A,  F,  F,  forged  and  thereafter  turned  and  pierced  at  the 
lathe  throughout  the  axis  of  the  arms.  The  horizontal  arm, 
AA,  carries  the  bolts,  BB,  screwed  to  its  two  extremities, 
suitably  tubulated,  in  which  the  sights  are  cemented  with 
marine  glue.  These  are  small  cylinders  of  crown  glass  or  of 
quartz,  with  good  plane  parallel  faces,  about  1  centimetre  in 
diameter  and  2  centimetres  long.  The  joint  with  the  gland  is 

71 


MEMOIRS    ON 


4>     § 

S   I 
J 


FIG.  6. — APPARATUS  FOR  THE  METHOD  OF  SIGHTS. 
FIG.  7. — PIEZOMETER  FOR  LIQUIDS. 
FIG.  8. — PIEZOMETER  FOR  GASES. 

72 


THE    LAWS    OF    GASES 

sealed  with  a  washer  of  celluloid.  The  piezometer  is  mounted 
symmetrically  with  the  axis  of  the  apparatus,  and  the  figure 
shows  a  piezometer  of  gas  in  place.  Its  reservoir  is  submerged 
in  mercury,  which  now  partially  fills  the  barrel.  Its  very  long 
stem  terminates  above  in  a  small  olive-shaped  reservoir  ending 
in  a  fine  point,  as  above.  Below  the  enlargement  is  the  gradu- 
ation, about  25  centimetres  long  and  made  of  very  delicate  cir- 
cular marks  narrowing  towards  the  top.  Little  globular  ex- 
pansions were  blown  out  between  them  along  the  lower  part  of 
the  stem,  with  the  object  of  virtually  increasing  the  total 
length  of  the  graduated  part.  The  piezometer  is  suspended 
from  its  upper  end  by  aid  of  a  small  pad  which  is  attached  to 
it  under  the  uppermost  bulb,  and  sustained  by  the  aid  of  a 
device,  BB,  CO,  shown  enlarged  in  a  separate  figure.  This 
piece  is  connected  at  CC  to  an  intermediate  stem  of  glass 
joined  in  the  same  way  at  its  upper  extremity  to  a  long  rod  of 
steel.  The  latter,  after  having  traversed  a  stuffing-box  charged 
with  leather  washers,  is  in  its  turn  joined  to  the  lower  end  of  a 
long  steel  screw.  This  is  movable  in  a  socket  of  brass  carried 
by  the  same  coupling  which  receives  the  leather  of  the  stuffing- 
box.  The  jacketed  barrel,  part  of  the  barrel  HH,  is  as  usual 
provided  with  a  stopcock  (not  shown),  through  which  the  in- 
itial pressures  are  applied  in  virtue  of  the  force-pump.  An- 
other tube  communicates  with  the  manometer.  In  place  of  the 
third  coupling,  which,  in  the  former  case,  supplied  the  electric 
current,  there  is  now  a  tube  of  steel  leading  to  a  special  steel 
reservoir,  to  which  the  device  for  producing  pressure,  former- 
ly described,  is  suitably  attached.  High  pressure  is,  therefore, 
brought  to  bear  at  this  place  by  manipulating  the  lower  screw. 

The  method  of  experimentation  will  now  be  intelligible 
without  much  further  explanation.  By  means  of  the  screw  at 
the  top  of  the  apparatus,  the  division -rings  on  the  stem  of 
the  piezometer  are  successively  placed  in  the  line  of  sight. 
Thereupon  pressure  is  applied  until  the  meniscus  appears 
flush  with  the  division  mark,  and  this  pressure  is  registered. 
The  readings  are  made  with  a  reading  telescope  well  centred 
in  the  line  of  sight,  and  the  field  of  vision  is  illuminated  with  a 
simple  gas-lamp  placed  on  the  opposite  side  in  the  same  direc- 
tion. This  light  is  quite  sufficient  as  long  as  certain  precau- 
tions are  taken  which  I  will  now  indicate.  The  injection  water 
rapidly  loses  its  transparency,  particularly  when  the  stem  is 

73 


MEMOIRS    ON 

heated.  Keading  thus  becomes  more  impossible  in  proportion 
as  the  layer  of  liquid  penetrated  by  the  rays  is  thicker.  To 
obviate  this  difficulty  I  at  first  placed  cylinders  of  crown-glass, 
plane-parallel  and  perfectly  transparent,  throughout  the  whole 
length  of  the  channel.  Readings  at  the  lower  temperatures 
were  then  easily  made,  but  at  the  higher  temperatures  the 
faces  of  the  glass  cylinder  were  rapidly  attacked  in  the  hot  re- 
gions and  after  a  time  covered  over  with  an  opaque  pulverulent 
layer,  being  thus  completely  corroded.  Hence,  in  subsequent 
work  I  replaced  the  crown-glass  cylinders  in  the  hot  parts  of 
the  tube  by  quartz  cylinders  with  their  faces  normal  to  the 
axis.  Readings  could  then  be  made  without  difficulty.  Again, 
to  avoid  the  decomposition  of  leather,  which  would  have 
clouded  the  internal  faces  of  the  sight-cylinders,  the  joints  in 
the  nuts  and  valves  were  sealed  with  celluloid  washers. 

The  different  temperatures  at  which  it  was  proposed  to  in- 
vestigate were  obtained  by  enveloping  the  arms  of  the  cross, 
AF,  by  an  appliance  adapted  to  do  service  either  as  a  water- 
bath  or  as  a  vapor-bath.  The  lower  part  of  this  surrounded 
the  three  arms  permanently,  the  seal  being  made  with  red-lead. 
The  upper  part  of  the  bath  differed  in  form  according  to  the 
uses  to  be  made  of  it,  and  it  was  fitted  into  a  shouldered  rim 
in  the  lower  part  and  held  in  place  by  friction. 

To  obtain  a  vapor-bath  an  appliance  with  a  two-chambered 
interior  was  at  hand,  provided  with  a  perforated  bottom.  The 
condenser  communicated  with  the  tubulure  F  of  the  removable 
lid,  which  at  the  same  time  furnished  a  support  for  the  ther- 
mometers. When  a  liquid  bath  was  wanted,  the  partition  was 
replaced  by  an  agitator  actuated  by  a  small  Gramme  machine. 
Constancy  of  temperature  was  then  obtained  by  suitably  ad- 
justing the  distance  and  the  gas  supply  of  the  crown  burner 
seen  at  the  bottom  of  the  bath. 

At  D,  under  the  leather  stuffing-box,  and  at  the  extremities, 
BB,  of  the  horizontal  arms,  small  water- jackets  were  added, 
fed  with  a  current  of  cold  water.  This  prevented  serious  over- 
heating of  the  leather  washers  or  of  the  mastic  seals  at  the 
sights.  The  discharge  water  flows  into  the  lower  reservoir, 
keeping  the  joints  of  the  cross,  which  are  plunged  in  it,  cold, 
and  then  escapes  by  a  lateral  tubulure. 

The  result  of  this  cooling  is  that  under  the  stuffing-box,  G, 
m  particular,  the  cross  reaches  the  temperature  of  the  bath 

74 


THE    LAWS    OF    GASES 

only  at  a  considerable  distance  below  the  lid.  I  thought  it 
worth  while  to  make  direct  tests  by  using  long,  probelike  ther- 
mometers specially  made  for  this  purpose,  in  order  to  be  prop- 
erly guided  as  to  the  maximum  height  up  to  which  the  tip  of 
the  piezometer  could  be  raised  at  any  temperature  without  en- 
countering seriously  reduced  values.  It  would  have  been  far 
preferable — indeed,  at  higher  temperatures,  it  would  be  abso- 
lutely necessary  to  close  the  cross  immediately  below  the 
stuffing-box,  and  to  produce  the  vertical  displacement  of  the 
piezometer  by  means  of  an  appropriate  appliance  attached  at 
the  lower  end.  All  this  is  feasible,  though  not  without  diffi- 
culty. 

PRELIMINARY    OPERATIOXS 

After  what  has  been  said  relatively  to  the  first  method,  only 
a  few  words  are  needed.  The  piezometers,  Figs.  7  and  8,  both 
for  liquids  and  for  gases,  do  not  differ  from  those  above  de- 
scribed except  as  to  the  stems,  which  now  carry  the  circular 
division  marks  in  place  of  the  platinum  filaments  formerly  used. 
They  are  filled  and  the  mass  of  the  contents  determined  in 
identically  the  same  way  as  before,  but  it  is  much  more  difficult 
to  adjust  them  in  place.  This  can  only  be  done  by  a  suitable 
pulley-block  fastened  to  the  ceiling,  by  means  of  which  the  cross 
may  be  raised  or  lowered  without  the  least  jolting.  Even  slight 
percussion  would  invariably  break  the  stem  of  the  piezometer. 

Constancy  of  temperature  is  now  reached  much  more  rapidly 
than  in  the  preceding  experiments,  whether  the  environment 
be  an  ice-bath,  a  water  or  a  vapor  bath  ;  for  the  total  mass 
which  is  to  reach  a  stationary  temperature  distribution  is 
enormously  smaller.  A  full  series  of  experiments  is  neverthe- 
less tediously  prolonged,  seeing  that  the  number  of  division 
marks  on  the  stem  is  so  much  larger  than  the  number  of  plati- 
num filaments  above.  As  far  as  100°  the  temperatures  were 
given  by  water-baths.  A  point  very  near  200°  corresponds  to 
the  boiling-point  of  methyl  benzoate,  another  at  260°  to  amyl 
benzoate.  Many  bodies  were  tested  as  to  their  availability  in 
vapor-baths  between  100°  and  200°.  For  140°  I  employed 
xylene  and  ethyl  acetate,  but  the  results  were  less  satisfactory 
than  in  the  preceding  cases.  I  was  quite  unable  to  obtain  a 
perfectly  constant  temperature  from  xylene.  The  specific 
heat  per  unit  of  volume  seems  to  be  very  small,  and  the  heat 

75 


MEMOIRS    ON 

transferred  insufficient  to  compensate  for  the  external  losses. 
I  shall  therefore  publish  the  series  made  at  this  temperature 
with  this  special  reservation. 

In  all  the  series  of  measurements  made  up  to  100°  by  this 
method,  I  restricted  the  observations  to  an  exact  number  of 
degrees,  using  thermometers  for  this  purpose  compared  in  ad- 
vance with  a  standard  provided  by  the  Bureau  International 
des  Poids  et  Mesures,  and  calibrated  by  M.  Guillaume.  They 
are  reduced  to  the  hydrogen  thermometer  by  means  of  the 
table  of  M.  Ohappuis.  At  100°  either  a  water-bath  or  a  steam- 
bath  was  available.  I  have  given  the  results  for  100°  exactly, 
the  interpolation  being  insignificant  and  no  error  resulting  from 
it.  Temperatures  above  100°  were  determined  by  means  of  ex- 
cellent thermometers  of  hard  glass,  constructed  by  M.  Chabaud, 
who  also  made  the  piezometers.  A  preliminary  comparison  of 
these  instruments  with  the  hydrogen  thermometer  showed  only 
very  small  differences,  for  which  allowance  was  made  through- 
out. There  is  no  room  here  to  give  the  data  for  this  calibra- 
tion, as  I  had  hoped  to  do;  but  I  took  into  account  the  displace- 
ment of  the  zero  mark  by  applying  a  special  test  .after  each 
series  of  measurements.  The  variations  of  this  point  were  small. 

However  complicated  the  apparatus  itself  may  appear,  the 
measurements  are  made  with  facility,  barring  accidents,  of 
course.  The  length  of  time  consumed  alone  made  them  te- 
dious. When  a  division  mark  has  been  brought  into  the  field 
of  the  telescope,  pressure  is  applied  until  the  mark  is  tangent 
to  the  mercury  meniscus,  which  here  appears  as  a  dark  demar- 
cation on  a  luminous  background.  The  adjustment  is  easily 
made  on  compressing  with  the  screw,  and  this,  as  in  the  pre- 
ceding work,  was  used  exclusively  whenever  the  pressures  ex- 
ceeded a  high  value.  Unfortunately,  at  high  temperatures  the 
action  of  the  water  eventually  tarnishes  the  external  surface 
of  the  graduated  stem,  and  the  meniscus  appears  blurred. 
Hence  it  is  always  necessary  to  stop  after  each  series  made  at 
the  higher  temperatures,  and  take  the  apparatus  apart  in  order 
to  lightly  repolish  the  stem.  The  operation  is  easily  accom- 
plished with  the  aid  of  a  polishing  wheel,  mounted  on  a  lathe. 
The  present  corrosion,  however,  is  not  to  be  compared  to  simi- 
lar experiences  with  crown-glass  mentioned  above.  It  is  for 
this  reason  that  hard  glass  piezometers  were  selected. 

Pressures  are  measured  in  the  way  described  above.  Ob- 

76 


THE    LAWS    OF    GASES 

viously,  account  must  be  taken  of  the  temperature  of  the  mer- 
cury column,  of  the  height  of  the  mercury  in  the  piezometer 
above  its  level  in  the  barrel,  and  of  the  position  of  this  level 
relatively  to  the  manometer. 

The  measurement  of  small  volumes  is  one  of  the  difficulties 
of  these  researches.  Without  entering  into  any  detail,  I  will 
simply  state  that  allowance  was  made  for  the  form  of  the  me- 
niscus, and  of  its  position  with  reference  to  the  division  mark 
during  calibration  and  during  the  subsequent  measurements. 
Only  in  the  case  of  gases  are  the  errors  here  in  question  to  be 
apprehended.  Their  volumes  diminish  with  extreme  rapidity, 
even  when  the  reservoirs  are  made  as  large  as  is  compatible 
with  the  dimensions  of  the  barrel. 


PART  II. — DATA  FOR  GASES 

The  results  summarized  by  the  following  tables  were  ob- 
tained in  experiments  of  the  kind  just  described. 

After  adding  all  corrections,  the  pressures  were  first  ex- 
pressed in  atmospheres.  To  find  the  corresponding  volumes, 
the  piezometer  may  be  supposed  to  be  standardized  at  0°  C., 
seeing  that  volume  ratios  alone  are  in  question.  Account  must 
be  taken,  however,  when  necessary,  of  the  temperature  differ- 
ences occurring  when  the  different  parts  of  the  piezometer  (stem 
and  reservoir)  were  calibrated.  The  corrections  due  to  thermal 
expansion  and  to  compression  were  afterwards  applied  in  their 
turn.  In  my  former  researches  I  have  given  all  the  necessary 
data. 

Having  found  the  mass  of  the  fluid  in  the  manner  stated 
above,  and  recalling  that  the  calibration  is  supposed  to  be  cor- 
rect at  zero,  all  the  subsequent  volumes  are  reduced  to  the 
value  they  would  have  if  the  given  mass  were  that  of  unit  of 
volume  at  0°  C.  and  1  atmosphere.  My  tables,  without  excep- 
tion, refer  to  this  unit.  Thereafter  I  constructed  a  series  of 
curves  corresponding  to  my  data,  in  which  pressures  are  the 
abscissas  and  the  products,  P  V,  of  pressure  and  volume  the 
ordinates.  From  these  curves  I  selected  a  series  of  correlated 
values  of  PV,  corresponding  to  groups  of  pressures  differing 
in  round  numbers  by  25,  50,  or  100  atmospheres,  and  from  them 
I  deduced  the  values  of  V.  For  carbon  dioxide  and  ethylene 
I  batched  the  data  in  smaller  pressure  intervals  because  of  the 

77 


MEMOIRS    ON 

complex  form  of  curve  observed  in  the  region  of  the  critical 
point.  Supplementary  tables  are  here  given. 

The  data  for  the  pressure  coefficient  are  taken  directly  from 
the  curves.  It  sufficed  to  draw  the  lines  of  equal  volume, 
which,  under  present  circumstances,  are  straight  lines  passing 
through  the  origin,  and  then  to  read  off  the  pressures  at  which 
these  lines  cut  the  successive  isotherms.  The  curves  were 
drawn  either  as  a  whole  or  by  distributing  them  on  sheets  of 
millimetre  cross-section  paper,  stretched  on  a  large  drawing- 
board  more  than  2  meters  broad. 

The  gases  studied  are  oxygen,  hydrogen,  nitrogen,  air,  car- 
bon dioxide,  and  ethylene.  The  last  were  operated  on  by  the 
method  of  sights  only  ;  the  other  gases  by  both  methods. 


RESULTS   OBTAINED    BY   THE    FIRST   METHOD 

(Method  of  Electric  Contacts) 

I  will  begin  with  the  results  of  the  first  method.  The  num- 
bers relating  to  pressures  below  500  atmospheres  belong  to  the 
series  of  data  obtained  by  the  second  method.  The  series 
found  by  the  method  of  contacts  does  not  begin  until  above 
500  or  600  atmospheres.  The  other  results  are  reproduced 
here  so  as  to  give  completed  series  at  zero. 

TABLE   4 


OXYGEN 

0°  C.     0°  C. 

15.6°  C. 

HYDR 

0°  C.      QO  C. 

OGEN 

15.4°  C. 

47.30  C. 

p 

PV 

FX10« 

FX106 

PV 

FX  106 

FX  106 

FxlOe 

Aim. 

1 

1.0000 

106 

— 

1  0000 

106 

— 

— 

100 

.9265 

9265 

— 

1.0690 

10690 

— 

— 

200 

.9140 

4570 



1.1380 

5690 

— 



300 

.9625 

3208 



1  2090 

403000 

— 



400 

1.0515 

2629 

— 

1.2830 

320700 

— 

— 

500 

1.1570 

2314 

— 

1.3565 

271300 

— 



600 

1.2702 

2117 

2228 

1.4322 

2387 

— 



700 

1.3867 

1981 

2075 

1.5050 

2150 

2234 



800 

1.5040 

1880 

1959 

1.5760 

1970 

2046 



900 

1.6200 

1800 

1871 

1.6515 

1835 

1895 

_ 

1000 

1.7360 

1736 

1800 

1.7250 

1725 

1778 

1893 

1100 

1.8502 

1682 

1740 

1.8007 

1637 

1685 

1785 

1200 

1.9620 

1635 

1689 

1.8690 

1557.5 

1604 

1694.5 

1300 

2.0722 

1594 

1645 

1.9383 

1491 

1533 

1617.5 

1400 

2.1798 

1557 

1605 

2.0048 

1432 

1472 

1551 

1500 

2.2890 

1526 

1571 

2.0700 

1380 

1418 

1493 

1600 

2.3960 

1497.5 

1540 

2.1352    1334.5 

1370 

1442 

1700 

2.5024 

1472 

1513.5 

2.20065 

1294.5 

1326 

1396 

78 

THE    LAWS    OF    GA 


TABLE  4. — Continued 


OXYGEN 

HYDROGEN 

0°  C.            0°  C. 

15.  6°  C. 

QO  C.             0°  C. 

15.  4°  C. 

47.3°  C. 

P 

PV 

FXlO* 

FX106 

PV 

FX106 

FX  10« 

FX106 

Atm. 

1800 

2.6073 

1448.5 

1488.5 

2.2644 

1258 

1288 

1354 

1900 

2.7113 

1427 

1465 

2.3275 

1225 

1254.5 

1316 

2000 

2.8160 

1408 

1444 

2.3890 

1194.5 

1222.5 

1280.5 

2100 

2.9190 

1390 

1424 

2.44965 

1166.5 

1194 

1249 

2200 

3.0217 

1373.5 

1406 

2.5102 

1141 

1168.5 

1220 

2300 

3.  1234 

1358 

1390 

2.5714 

1118 

1144.5 

1194.5 

2400 

3.2244 

1343.5 

1374 

2.6340 

1097.5 

1122.5 

1170.5 

2500 

3.32375 

1329.5 

1360 

2.6950 

1078 

1101 

1148 

2600 

3.4229 

1316.5 

1346 

2.7547 

1059.5 

1082.5 

1126.5 

2700 

3.5208 

1304 

1332 

2.8134 

1042 

1063 

1107 

2800 

3.6176 

1292 

1319.5 

2.8686 

1024.5 

1045 

1088 

2900 

3.7120 

1280 

1307 

— 

— 

1028 

1071 

3000 

— 

— 

1296 

— 

— 

1012.8 

— 

TABLE   5 


NITKOGE 
0°  C.     0°  C. 

N 
16.0°  C. 

43.  6°  C. 

A 
0°  C.     0°  C. 

IR 

15.  7°  C. 

45.10°C. 

PV 

FX  io« 

FX106 

FX  106 

PV 

FX  106 

FX  106 

FX  106 

1.0000 

106 

_ 

1.0000 

106 

.9910 

9910 

— 

— 

.9730 

9730 





1.0390 

5195  ' 

— 

— 

1.0100 

5030 





1.1360 

3786 

— 

— 

1.0975 

3658 





1.2570 

3142 

— 

— 

1.2145 

3036 





1.3900 

2780 

— 

— 

1.3400 

2680 





1.5260 

2543 

— 

— 

1.4700 

2450 





1.6625 

2375 

— 

— 

1.6037 

2291 

2384 



1.8016 

2252 

2331 

— 

1.7368 

2171 

2251.5 

2387.5 

1.9368 

2152 

2224 

2354 

1.8675 

2075 

2147 

2271 

2.0700 

2070 

2134 

2242 

1.9990 

1999 

2061.5 

2176.5 

2.20385 

2003.5 

2062 

2162 

2.1329 

1939 

1992 

2097 

2.3352 

1946 

2000 

2095 

2.2596 

1883 

1933 

2030 

2.46545 

1896.5 

1945 

2035 

2.3842 

1834 

1880 

1970 

2.5942 

1853 

1897 

1982 

2.5081 

1791.5 

1834 

1917 

2.72025 

1813.5 

1854 

1933 

2.6310 

1754 

1793.5 

1871.5 

2.8456 

1778.5 

1818 

1891.5 

2.7528 

1720.5 

1757 

1832.5 

2.9665 

1745 

1784 

1853.5 

2.87385 

1690.5 

1725 

1796.5 

3.0861 

1714.5 

1752 

1817.5 

2.9916 

1662 

1695 

1762.5 

3.20815 

1688.5 

1724.5 

1787.5 

3.1103 

1637 

1668 

1733 

3.3270 

1663.5 

1699 

1758.5 

3.2260 

1613 

1643 

1705 

3.4461 

1641 

1675 

1731.5 

3.34005 

1590.5 

1629 

1678.5 

3.5640 

1620 

1653 

1707 

3.4540 

1570 

1598 

1654 

3.6823 

1601 

1632 

1683.5 

3.56615 

1550.5 

1578 

1632.5 

38004 

1583.5 

1613.5 

1663.5 

3.6804 

1533.5 

1559.5 

1612 

3.9200 

1568 

1596 

1644 

379125 

1516.5 

1542 

1593.5 

4.0378 

1553 

1579 

1626 

3.9000 

1500 

1525 

1575.5 

4.1553 

1539 

1564 

1608 

4.00815 

1484.5 

1510 

1557.5 

4.2700 

1525 

1549.5 

1592 

4.1146 

1469.5 

1495 

1541 

4  3558 

1502 

1536 

1577 

42195 

1455 

1480.5 

1525 

4.4970 

1499 

1522.5 

1563 

43230 

1441 

1466 

1509.5 

Atm. 

1 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1000 

1100 

1200 

1300 

1400 

1500 

1600 

1700 

1800 

1900 

2000 

2100 

2200 

2300 

2400 

2500 

2600 

2700 

2800 

2900 

3000 


79 


MEMOIRS    ON 

The  following  tables  contain  the  data  needed  for  the  calcula- 
tion of  the  pressure  coefficients.  They  show  the  pressures  at 
which  the  unit  of  mass  occupies  the  volumes  given  in  the  first 
column  at  the  stated  temperatures  : 


TABLE  6. — PRESSURES   AT   CONSTANT   VOLUME 


CONSTANT 
VOLUME 

OXYGEN 
0°C. 

15.  6°  C. 

CONSTANT 
VOLUME 

HYDRC 

o°c. 

>GEN 

15.4°  C. 

47.3°  C. 

FxlO6 
2117 
1880 
1736 
1635 
1497.5 
1408 
1343.5 
1304 

Aim. 
600 
800 
1000 
1200 
1600 
2000 
2400 
2700 

Aim. 
669 
888 
1106 
1325 
1765 
2188 
2618 
2925 

FxlO6 
1725 
1557.5 
1380 
1258 
1194.5 
1097.5 
1024.5 

Aim. 
1000 
1200 
1500 
1800 
2000 
2400 
2800 

Aim,: 
1055 
1264 
1579 
1889 
2099 
2518 
1925 

Atm. 
1164 
1390 
1737 
2071 
2300 
2746 

CONSTANT 
VOLUME 

NITRO< 

0°('. 

^EN 

16.0°  C 

43.6°  C. 

CONSTANT 
VOLUME 

All 

o°c. 

i 

15.7°  C. 

45.1°  C. 

FxlO6 

Atm. 

Atm. 

Atm. 

FxlO6 

Atm. 

Atm. 

Atm. 

2070 

1000 

1088 

1239 

2171 

800 

876 

1007 

1946 

1200 

1298 

1474 

1999 

1000 

1089 

1250 

1813.5 

1500 

1613 

1812 

1883 

1200 

1295 

1474 

1714.5 

1800 

1937 

2168 

1754 

1500 

1610 

1828 

1663.5 

2000 

2150 

2401 

1662 

1800 

1924 

2166 

1583.5 

2400 

2572 

2858 

1613 

2000 

2131 

2394 

1525 

2800 

2990 

— 

1533.5 

2400 

2552 

2846 

RESULTS   OBTAINED    BY   THE    SECOND    METHOD 

(Method  of  Sights) 

The  following  tables  of  results  obtained  by  the  second 
method  are  arranged  like  the  preceding,  except  that  only  the 
products  P  V  are  given  for  all  the  series  : 

80 


THE    LAWS    OF    GASES 


TABLE  7. — OXYGEN" 


Atm. 
1 

100 
150 
200 
250 
300 
350 
400 
450 
500 
550 
600 
650 
700 
750 
800 
850 
900 
950 
1000 


o°c. 

15.65°  C. 

99.500  C. 

199.50  c. 

PV 

FX106 

PV 

FX106 

PV 

Fxios 

PV 

FXIO« 

1.0000 

106 

.9265 

9265 

1.0045 

10045 

1.3750 

13750 





.9135 

6090 

.9920 

6613 

1.3820 

9213 

1.8000 

12000 

.9140 

4570 

.9945 

4972 

1.4000 

7000 

1.8190 

9095 

.9315 

3726 

1.0135 

4054 

.4240 

5696 

1.8500 

7400 

.9625 

3208 

1.0420 

3473 

.4530 

4843 

1.8850 

6283 

1  0040 

2869 

1.0800 

3086 

.4900 

4257 

1.9220 

5491 

1.0515 

2629 

1.1250 

2812 

.5320 

3830 

1.9610 

4902 

1.1025 

2450 

1.1750 

2611 

.5760 

3502 

2.0040 

4453 

1.1560 

2312 

1.2270 

2454 

.6220 

3244 

2.0500 

4100 

1.2120 

2204 

1.2815 

2330 

.6690 

3035 

2.0950 

3809 

1.2690 

2115 

1.3370 

2228 

.7200 

2867 

2.1420 

3570 

1.3275 

2042 

1.3940 

2144 

.7725 

2727 

2.1910 

3371 

1.3855 

1979 

1.4515 

2073 

.8270 

2610 

2.2415 

3202 

1.4440 

1925 

1.5080 

2011 

.8810 

2508 

22920 

3056 

1.5030 

1879 

1.5660 

1957 

.9340 

2417 

2.3430 

2929 

1.5615 

1841 

1  6240 

1911 

1.9875 

2338 

2.3950 

2812 

1.6200 

1800 

1.6820 

1869 

2.0415 

2268 

2.4465 

2718 

1.6780 

1766 

1.7400 

1831 

2.0960 

2206 

2.4980 

2629 

1.7355 

1735 

1.7980 

1798 

2.1510 

2151 

— 

— 

TABLE  8. — HYDROGEN 


p 

o°c. 

15.50°  C. 

99.25°C. 

200.  25°  C. 

PV 

Fxioe 

PV 

FX106 

PV 

FX106 

PV 

FX106 

Atm. 

1 

1.0000 

106 













100 

1.0690 

10690 

1.1290 

11290 









150 

1.1030 

7353 

1.1630 

7753 

1.4770 

9846 

1.8480 

12320 

200 

1.1380 

5690 

1.1980 

5990 

1.5135 

7567 

1.8840 

9420 

250 

1.1730 

4692 

1.2350 

4940 

1.5500 

6200 

1.9200 

7680 

300 

12090 

4030 

1.2685 

4228 

1.5860 

5286 

1.9560 

6520 

350 

1.2460 

3560 

1.3050 

3728 

1.6225 

4636 

1.9930 

5694 

400 

.2830 

3207 

1.3410 

3352 

1.6590 

4147 

2.0300 

5075 

450 

.3200 

2933 

1.3780 

3062 

1.6950 

3766 

2.0670 

4593 

500 

.3565 

2713 

1.4150 

2830 

1.7310 

3462 

2.1050 

4210 

550 

.3935 

2533 

1.4520 

2640 

1.7675 

3214 

2.1400 

3891 

600 

.4315 

2386 

1.4890 

2482 

1.8040 

3006 

2  1762 

3627 

650 

1.4685 

2259 

1.5260 

2347 

1.8400 

2831 

2.2120 

3403 

700 

1.5045 

2149 

1.5620 

2231 

1.8760 

2680 

2.2480 

3211 

750 

1.5400 

2053 

1.5985 

2131 

1.9130 

2551 

2.2840 

3045 

800 

1.5775 

1972 

1.6340 

2042 

1.9490 

2436 

2.3200 

2900 

850 

1.6140 

1879 

1.6690 

1964 

1.9860 

2336 

2.3560 

2772 

900 

1.6490 

1832 

1.7060 

1896 

2.0210 

2244 

2.3915 

2657 

950 

1.6850 

1774 

1.7410 

1832 

20660 

2174 





1000  1.7200 

1720 

1.7760 

1776 

2.0930 

2093 

— 

— 

81 


MEMOIRS    ON 


TABLE  9. — NITROGEN 


p 

o°c. 

16.03°  C. 

99.45°C. 

199.500  C. 

PV 

Fxioe 

PV 

FXIO« 

PV 

FX106 

PV 

FX10« 

Aim. 

1 

1.0000 

10' 

— 

— 

— 

— 

— 

— 

100 

.9910 

9910 

1.0620 

10620 

— 

— 

— 

— 

150 

1.0085 

6723 

1.0815 

7210 

1.4500 

9666 

1.8620 

12410 

200 

1.0390 

5195 

.1145 

5572 

1.4890 

7445 

1.9065 

9532 

250 

1.0825 

4330 

.1575 

4630 

1.5376 

6150 

1.9585 

7834 

300 

1.1360 

3786 

.2105 

4035 

1.5905 

5301 

2.0145 

6715 

350 

1.1950 

3414 

.2675 

3621 

1.6465 

4703 

2.0730 

5923 

400 

1  2570 

3142 

.3290 

3322 

1.7060 

4265 

2.1325 

5331 

450 

1.3230 

2940 

.3940 

3098 

1.7665 

3924 

2.1940 

4875 

500 

1.3900 

2780 

.4590 

2918 

1.8275 

3655 

2.2570 

4514 

550 

1.4585 

2652 

.5265 

2775 

1.8900 

3436 

2.3200 

4218 

600 

1.5260 

2543 

.5945 

2657 

1  9545 

3258 

2.3840 

3973 

650 

1.5935 

2452 

.6615 

2556 

2.0200 

3108 

2.4485 

3613 

700 

1.6615 

2374 

.7290 

2470 

£.0865 

2980 

2.5125 

3589 

750 

1.7300 

2307 

.7975 

2397 

2.1535 

2871  - 

2.5765 

3435 

800 

1.7980 

2247 

1.8655 

2332 

2.2200 

2775 

2.6400 

3300 

850 

1.8660 

2195 

1.9330 

22,74 

2.2865 

2690 

2.7060 

3184 

900 

1.9340 

2149 

2.0015 

2224 

2.3540 

2616 

2.7715 

3079 

950 

2.0015 

2107 

2.0690 

2178 

2.4230 

2550 

2.8380 

2987 

1000 

2.0685 

2068 

2.1360 

2136 

— 

— 

— 

— 

TABLE  10. — AIR 


P 

0  C. 

15.70°  C. 

99.40°  C. 

200.  4°  C. 

PV 

FXIO« 

PV 

Fxio« 

PV 

FX106 

PV 

FX106 

Aim. 

1 

1.0000 

106 

— 

— 

— 

— 

— 

— 

100 

.9730 

9730 

1.0460 

10460 

1.4030 

14030 

— 

— 

150 

.9840 

6560 

.0580 

7053 

1.4310 

9540 

1.8430 

12290 

200 

1.0100 

5050 

.0855 

5427 

.4670 

7335 

1.8860 

9430 

250 

1.0490 

4196 

.1260 

4504 

.5110 

6044 

1.9340 

7736 

300 

1.0975 

3658 

.1740 

3913 

.5585 

5195 

1.9865 

6622 

350 

1.1540 

3297 

.2250 

3500 

.6085 

4596 

2.0410 

5831 

400 

1.2145 

3036 

.2835 

3209 

.6625 

4156 

20960 

5240 

450 

1.2765 

2837 

.3460 

2991 

.7200 

3822 

2.1530 

4785 

500 

1.3400 

2680 

1.4110 

2822 

.7815 

3563 

2.2110 

4422 

550 

1.4040 

2553 

1.4740 

2680 

1.8440 

3353 

2.2700 

4127 

600 

14700 

2450 

1.5375 

2563 

1.9060 

3177 

2.3300 

3883 

650 

1.5365 

2363 

1.6015 

2464 

1.9670 

3026 

2.3900 

3677 

700 

1.6020 

2288 

1.6670 

2381 

2.0300 

2900 

2.4515 

3502 

750 

1.6690 

2225 

1.7340 

2312 

2.0930 

2790 

2.5130 

3351 

800 

1.7345 

2168 

1.8000 

2250 

2.1555 

2694 

2.5750 

3219 

850 

1.7990 

2116 

1.8655 

2194 

2.2180 

2609 

2.6370 

3102 

900 

1.8640 

2071 

1.9300 

2144 

2.2830 

2537 

2.7000 

3000 

950 

1.9280 

2030 

1.9960 

2101 

2.3490 

2473 

2.7640 

2903 

1000 

1.9920 

1992 

2.0600 

2060 

2.4150 

2415 

2.8280 

2828 

82 


THE    LAWS    OF    GASES 

I  shall  insert  here  also  certain  supplementary  results  obtained 
from  these  curves,  which  will  be  found  useful  in  correcting  the 
readings  of  gas  manometers.  To  these  I  append  the  results  of 
experiments  made  in  1864  at  Fourvieres  with  the  same  end  in 
view : 


TABLE    10   (2). — VOLUMES 
(Same  Unit  of  Mass  as  Heretofore) 


p 

OXYGEN  AT 
15.65°  0. 

FxlO6 

H  YDROGEN  AT 
15.50°  C. 

FxlO6 

NITROGEN  AT 
16  05°  C. 

FxlO6 

AIR  AT 

15.70°  C. 
FxlO6 

125  Aim. 
175  " 
225  " 
275  " 
325  " 
375  " 
425  " 
475  " 

7976 
'  5663 
4456 
3735 
3261 
2939 
2706 
2528 

9168 
6746 
5411 
4552 
3959 
3528 
3199 
2940 

8560 
6255 
5044 
4298 
3790 
3460 
3205 
3003 

8400 
6114 
4907 
4178 
3689 
3343 
3094 
2900 

TABLE  11. — EXPERIMENTS   AT   FOURVIERES 

(Values  of  PV at  \§°) 


PRESSURES   IN 
METERS 


,76 


20 
25 
30 
35 
40 
45 
50 
55 
60 
65 


NITROGEN 

AIR 

1.0000 

1.0000 

.9930 

.9901 

.9919 

.9876 

.9908 

.9855 

.9899 

.9832 

.9896 

.9824 

.9895 

.9815 

.9897 

.9808 

.9902 

.9804 

.9908 

.9803 

.9913 

.9807 

83 

MEMOIRS    ON 


TABLE  12. — DATA   FOR  THE   COMPUTATION   OF  THE  COEFFI- 
CIENTS  OF   PRESSURE 

(Pressure  at  Constant  Volume) 


CONSTANT 

OXYGKN 

CONSTANT 

HYDROGEN 

VOLUME 

0°C. 

16.65°C. 

99.50°C. 

199.  50°  C. 

VOLUME 

0°  C. 

15.5°C. 

99.25°C. 

2(;0.2C°C. 

rxio6 

Atm. 

Atm. 

Atm. 

Atm. 

FX10« 

Aim. 

Atm. 

Atm. 

Atm. 

9205 

100 

108 

149 

196 

10690 

100 

106 

137 

174 

6090 

150 

163 

233 

312 

7353 

150 

159 

207 

262 

4570 

200 

219 

322 

437 

5690 

200 

212 

276 

351 

3726 

250 

276 

415 

566 

4692 

250 

265 

345 

439 

3208 

300 

332 

508 

698 

4030 

300 

318 

414 

528 

2869 

350 

388 

598 

827 

3560 

350 

370 

482 

614 

2629 

400 

446 

691 

— 

3207 

400 

423 

551 

700 

2450 

450 

502 

781 

— 

2933 

450 

476 

620 

788 

2312 

500 

558 

868 

— 

2713 

500 

530 

688 

874 

2204 

550 

624 

953 

— 

2533 

550 

582 

756 



2386 

600 

635 

824 



2259 

650 

687 

891 



,  2149 

700 

741 

960 

— 

CONSTANT 
VOLUME 

NITROGEN 

CONSTANT 
VOLUME 

AIR 

0°C. 

16.03°C. 

99.4.r>oc. 

199.5°  C. 

o°c. 

15.70°C. 

99.40°C. 

200.40°  C. 

FX106 

Atm. 

Atm. 

Atm, 

Atm. 

FX10« 

Atm. 

Atm. 

Atm. 

Atm. 

9910 

100 

107 

146 

192 

9730 

100 

107 

146 

193 

6723 

150 

162 

225 

299 

6560 

150 

162 

227 

303 

5195 

200 

217 

307 

414 

5050 

200 

217 

310 

420 

4330 

250 

273 

392 

530 

4196 

250 

373 

395 

538 

3786 

300 

328 

474 

644 

3658 

300 

329 

479 

655 

3414 

350 

383 

556 

758 

3297 

350 

383 

564 

770 

3142 

400 

439 

637 

869 

3036 

400 

439 

646 

881 

2940 

450 

494 

718 

— 

2837 

450 

495 

728 

993 

2780 

500 

548 

797 

2680 

500 

550 

807 

— 

2652 

550 

602 

875 

2553 

550 

603 

887 

— 

2543 

690 

656 

957 

2450 

600 

658 

970 

— 

The  following  tables  relative  to  carbon  dioxide  and  ethylene 
contain  the  .valueSxOi  .the  products  P  V  only  : 


THE    LAWS    OF    GASES 


TABLE  13. — VALUES   OF   PV    FOR   CARBON    DIOXIDE 


p 

o°c. 

10°  C. 

20°  C. 

30°  C. 

40°  C. 

50°  C. 

60°  C. 

Atm. 

1 

1.0000 

— 



— 



— 

— 

50 

.1050 

.1145 

.6800 

.7750 

.8500 

.9200 

.9840 

75 

.1530 

.1630 

.1800 

.2190 

.6200 

.7470 

.8410 

100 

.2020 

.2130 

.2285 

.2550 

.3090 

.4910 

.6610 

125 

.2490 

.2620 

.2785 

.3000 

.3350 

.3950 

.5100 

150 

.2950 

.3090 

.3260 

.3460 

.3770 

.4190 

.4850 

175 

.3405 

.3550 

.3725 

.3930 

.4215 

.4570 

.5055 

200 

.3850 

.4010 

.4190 

.4400 

.4675 

.5000 

.5425 

225 

.4305 

.4455 

.4655 

.4875 

.5130 

.5425 

.5825 

250 

.4740 

.4900 

.5100 

.5335 

.5580 

.5865 

.6250 

275 

.5170 

.5340 

.5545 

.5775 

.6040 

.6330 

.6675 

300 

.5595 

.5775 

.5985 

.6225 

.6485 

.6765 

.7100 

350 

.6445 

.6640 

.6850 

.7090 

.7365 

.7650 

.7980 

400 

.7280 

.7475 

.7710 

.7950 

.8230 

.8515 

.8840 

450 

.8090 

.8310 

.8550 

.8800 

.9075 

.9365 

.9690 

500 

.8905 

.9130 

.9380 

.9630 

.9900 

1.0210 

1.0540 

550 

.9700 

.9935 

1.0200 

.0465 

1.0740 

1.1035 

1.1370 

600 

1.0495 

1.0730 

1.0995 

.1275 

1.1570 

1.1865 

1.2190 

650 

1.1275 

1.1530 

1.1800 

.2075 

1.2375 

1.2680 

1.3010 

700 

1.2055 

1.2320 

1.2590 

.2890 

1.3190 

1.3500 

1.3825 

750 

1.2815 

1.3105 

1.3395 

.3700 

1.4000 

1  4315 

1.4640 

800 

1.3580 

1.3870 

1.4170 

.4475 

1.4790 

1.5105 

1.5435 

850 

1.4340 

1.4625 

1.4935 

.5245 

1.5570 

1.5885 

1.6225 

900 

1.5090 

1.5385 

15685 

.6000 

1.6325 

1.6650 

1.6995 

950 

1.5830 

1.6115 

1.6430 

6740 

1.7065 

1.7395 

1.7745 

1000 

1.6560 

1.6850 

1.7160 

1.7480 

1.7800 

1.8140 

1.8475 

r 

70°  C. 

80°  C. 

90°  C. 

]00°C. 

137°  C. 

198°  C. 

258°  C. 

Atm. 

1 











— 



50 

1.0430 

1.0960 

1.1530 

1  2065 

1.3800 

— 

_ 

75 

.9180 

.9880 

1.0515 

1.1180 

1.3185 

1.6150 

1.8670 

100 

.7770 

.8725 

.9535 

1.0300 

1.2590 

15820 

1.8470 

125 

.6430 

.7590 

.8580 

.9470 

1.2050 

1.5530 

1.8310 

150 

.5750 

.6805 

.7815 

.8780 

1.1585 

1.5295 

1.8180 

175 

.5730 

.6515 

.7410 

.8320 

1.1230 

1.5100 

1.8095 

200 

.5955 

.6600 

.7315 

.8145 

1.0960 

1.4960 

1.8040 

225 

.6285 

.6815 

.7460 

.8175 

1.0835 

1.4890 

1.8035 

250 

.6670 

.7135 

.7690 

.8355 

1.0810 

1.4870 

1.8060 

275 

.7070 

.7515 

.8015 

.8600 

1.0885 

1.4875 

1.8115 

300 

.7485 

.7900 

,8375 

.8900 

1.1080 

1.4935 

1.8200 

350 

.8325 

.8725 

.9135 

.9615 

1.1565 

1.5210 

1.8465 

400 

.9180 

.9560 

.9660 

1.0385 

1.2175 

1.5630 

1.8830 

450 

1.0035 

1.0400 

1.0775 

1.1190 

1.2880 

1.6160 

1.9280 

500 

1.0880 

1.1240 

1.1610 

1.2005 

1.3620 

1.6775 



550 

1.1720 

1.2085 

1.2430 

1.2830 

1.4400 

1.7450 



600 

1.2540 

1.2900 

1.3265 

1.3655 

1.5180 

'  1.8120 

— 

650 

1.3360 

1.3725 

1.4085 

1.4475 

1.5960 

1.8835 

— 

700 

1.4170 

1.4535 

1.4900 

1.5285 

1.6760 

1.9560 

— 

750 

1.4985 

1.5335 

1.5705 

1.6100 

1.7565 

2.0330 

— 

800 

1.5780 

1.6140 

1.6505 

1.6890 

1.8355 

21080 

— 

850 

1.6575 

1.6925 

1.7285 

1.7680 

1  9150 

21860 

— 

900 

1.7345 

1.7710 

1.8075 

1.8460 

1.9940 

2.2600 

— 

950 

1.8100 

1  8470 

1.8845 

1.9230 

2.0720 

2.8350 

— 

1000 

1.8840 

1.9210 

1.9590 

1.9990 

— 

— 

— 

85 


MEMOIRS  ON 


Atm. 

31 

33 

34 

35 
»  37 

40 

44 

45 

48 

50 

53 

55 

56 

57 

60 

65 

68 

70 

71 

72 

73 

74 

75" 

78 
80 

85 

95 
100 
110 


TABLE  14.  —  CARBON   DIOXIDE 

(Supplementary  Table  for  Values  of  PV) 

0° 

100 

200 

30° 

32° 

350 

400 

50° 

600 

700 

80° 

90° 

1000 

.7380 

7  1  on 

7860 

.  f  IzU 

.  6990 
.0750 

^7640 

.8350 







— 

_ 











.0790 

.7420 

.8170 

.8820 





__ 

— 











.7060 

.7895 

.8590 

.8750 

.8920 

.9235 















.6530 

.7490 























.1050 

.7380 

.8190 

.8350 

.8555 

.8880 

.9520 

1.0110 

1.0660 









.7060 

.7930 





.8670 

.9330 

.9950 

1.0520 







1.1050 

.1145 

.6800 

.7750 

.7920 

.8155 

.8525 

.9210 

.9840 

1.0430 

1.0980 

1.1535 

1.2070 

.6370 

.7460 



— 

.8300 

.9020 

.9680 

1.0280 

1.0850 

1.1420 

1.1960 





.6050 

.7260 

.7455 

.7720 

.8135 

.8890 

.9570 

1.0185 

1.0760 

1.1340 

1.1785 





.5850 





— 

— 

— 

— 

— 



— 

— 





.1480 





— 

— 

— 



— 









.1520 

.6680 

.6935 

.7245 

.7720 

.8555 

.9285 

.9940 

1.0540 

1.1130 

1.1710 





.5950 

.6290 

.6690 

.7260 

.8200 

.8990 

.9690 

1.0325 

1.0930 

1.1530 







.5350 

.5780 

.6310 

.6950 

.7970 

.8810 

.9530 

1.0190 

1.0810 

1.1420 

— 

— 

— 

.4700 
2300 

.5400 

.6020 

.6730 

.7820 

.8685 

.9430 

1.0100 

1.0730 

1.1350 

~ 

_ 



.2230 

.4910 

























.4600 

— 

— 

— 

— 

— 







— 

— 

—  • 

.2190 

.4050 

.5310 

— 

— 

— 

— 

— 

— 

— 

_ 

_ 

.2190 

.2680 

.5100 

.6130 

.7410 

.8360 

.9170 

.9880 

1.0535 

1.1180 

_ 

.2205 

.2410 

.4200 





_ 



_ 

_ 

_ 







.2225 



.3180 

.5400 

.7000 

.8030 

.8900 

.9660 

1.0335 

1.1005 

2810 

5030 

_ 

_ 

_ 

_ 

.2670 

.4350 

•6510 

.7690 

.8630 

.9425 

1.0135 

1.0835 









— 

.2650 

.3410 

.5990 

.7340 

.8350 

.9190 

.9935 

1.0655 













.3140 

.5460 

.6980 

.8060 

.8960 

.9735 

1.0480 











— 

.3090 

.4910 

.6610 

.7770 

.8720 

.9540 

1.0305 

— 

— 

— 

— 

— 

— 

.3130 

.4170 

.5880 

.7210 

.8240 

.9140 

.9970 

[Tor  Table  15,  see  p.  87.] 


TAI 
P 

JLE  1 

0° 

6.— 

50 

3UPP 

7.50 

LEMJ 

10° 

EKT^ 
20° 

LEY  •• 
30° 

VALL 

40° 

'ES  C 

50° 

>F  PI 

60° 

7  FOI 

T0° 

1  ET1 

80° 

IYLE 

90° 

NE 
100° 

Atm. 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
4i> 
47 
48 
49 
50 
51 
52 
53 
54 
56 
58 
60 
65 
70 
75 
80 
90 
100 

.6340 
.6165 
.5955 

.5330 
.1610 
.1570 
.1580 
.1600 

.1645 
.1095 
.1755 
.1810 

.2025 

.2425 
.2565 

,3100 

.6490 
.6155 

.6735 
.6425 

.6820 
.6685 

— 

— 

- 

- 

- 

— 



- 

.5730 
.5470 
.5150 
.4770 
.1890 
.1850 
.  1855 
.  1875 
.  1900 

.1945 

.2050 
.2145 

.2535 

.6085 

.6370 

.7320 

- 

— 

- 

— 

- 

- 

— 

- 

.5675 

.5100 
.4670 
.3300 
.  2150 
.2075 

.2060 

.6030 
.5620 

.5075 
.4700 
.4200 
.2900 
.2400 

.6980 
.6840 

.6290 
.5975 

.7310 

.8300 
.8140 

.8865 

- 

\ 

- 

- 

- 

.2090 
.2125 
.5180 

.2290 
.2270 
.2285 
.2315 

.2655 
.2785 

.3303 

.5610 
.5235 
.4805 
.4300 
.3310 
.3110 
.3110 
.3165 
.3370 
.3  GOO 

.6905 

.6195 
.5500 
.4830 
.4300 
.3990 
.3915 
.4030 

.7810 

.7285 
.  6805 
.6310 
.5805 
.5390 
.4875 
.4710 

86 

.8595 

.8170 

.7430 
.7045 
.6660 
.6060 
.5665 

.9290 

.8925 

.8315 
.8000 
.7670 
.7090 
.6680 

.9850 
.9630 

.9090 
.8815 
.  8555 
.8035 
.7620 

1.0285 

.9795 
.9550 
.9310 
.8840 
.8465 

1.0920 

1.0260 
1.0050 

.9265 

1.1530 

1.0940 
1.0755 

1.0050 

THE    LAWS    OF    GASES 


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87 


MEMOIRS    ON 


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THE    LAWS    OF    GASES 


EXAMINATION   OF   THE   KESULTS 

General  Laws 

An  inspection  of  the  above  results  will  lead  to  inferences 
similar  in  a  general  way  to  those  which  I  adduced  in  my 
memoir  of  1881.  I  shall  now,  moreover,  be  able  to  examine  a 


2.00 
1.90 
1.80 
1.70 
1.60 
1.50 
1.40 
1.30 
1.20 
1.10 
1.00 
0.90 
0.80 
0.70 
0.60 
0.50 
0.40 
0.30 
0.20 
0.10 


Atm.  P.100 


200 


300 


400    500    600 

FIG.  9. 


700 


800 


900 


1000 


great  number  of  moot  points,  relative  to  which  no  decision 
could  certainly  have  been  made  by  aid  of  investigations  no 
more  extensive  than  those  heretofore  available. 

It  did  not  seem  necessary  to  give  all  the  curves  for  the  divers 


MEMOIRS    ON 


gases,  seeing  that  the  principal  types  were  drawn  in  full  in  my 
first  research.  The  group  of  isotherms  for  carbon  dioxide 
graphically  represented  within  the  limits  actually  reached  suf- 
fice for  exhibiting  the  results  in  their  general  features.  The 
first  diagram  (Fig.  9)  shows  the  isotherms  for  this  gas,  when 
the  pressures  are  laid  off  as  abscissas  and  the  products  PFas 
ordinates.  The  second  diagram  (Fig.  10)  shows  the  region  in 


2.00 1 


T.75 _ 


1.50 


1.25 


J.OO 


0.75 


0.50  - 


0.25 


Atm.  P.    25 


250 


the  neighborhood  of  the  critical  point  with  more  detail.  The 
part  of  the  isotherms  represented  by  dotted  lines  has  been 
added  merely  to  round  off  the  figures.  They  have  not  been 
made  the  subject  of  measurement  in  the  present  paper,  except- 
ing the  lines  for  32°  and  35°,  which  are  dotted  throughout. 

At  temperatures  lower  than  the  critical  point,  a  part  of  the 
isotherms  is  in  the  form  of  straight  vertical  lines,  correspond- 
ing to  liquefaction.  These  did  not  occur  in  my  first  group  of 
curves,  which  began  at  35°. 

The  ordinates  of  the  extremities  of  each  straight  part  show 

90 


THE    LAWS    OF    GASES 


the  volume  in  the  liquid  state  and  the  corresponding  volume 
of  the  saturated  vapor,  and  hence,  also,  the  densities  of  the  two 
states,  respectively.  The  locus  of  these  points  is  Andrews's 
curve  of  liquefaction,  and  has  been  traced  in  the  second  dia- 
gram (Fig.  10).  Another  dotted  curve,  recalling,  as  does  the 
preceding,  the  form  of  a  parabola  between  the  limits  of  con- 
struction, is  the  locus  of  the  points  of  minimum  ordiriates,  P  V. 
The  abscissas  of  this  curve  pass  through  a  maximum,  as  was  to 
be  anticipated  from  the  facts  which  I  have  already  indicated 
elsewhere — i.e.,  for  gases  in  a  region  remote  from  their  critical 
points,  like  methane,  air,  nitrogen,  the  abscissa  of  the  mini- 
mum ordinate  shows  a  retrograde  march  for  continually  in- 
creasing temperatures,  an  inversion  of  what  took  place  in  the 
case  of  carbon  dioxide  within  the  field  to  which  I  was  then  re- 
stricted. The  following  table  gives  the  maximum  vapor  ten- 
sion, the  pressure  corresponding  to  the  minimum  ordinates  at 
the  different  temperatures,  as  well  as  the  value  of  PFat  that 
ordinate  for  the  gases  oxygen,  carbon  dioxide,  and  ethyl ene  : 

TABLE  19 


VALUES  OF  PV 

VAPOR 
TENSION 

T 

CARBON  DIOXIDE 

ETHYLENE 

OXYGEN 

CARB. 
DIOX 

ETHY- 
LENE 

P 

PV 

P 

PV 

P 

PV 

P 

P 

~"c~ 

Aim. 

Aim. 

Aim. 

Aim. 

Aim. 

0° 

34.5 

.0740 

42 

.1570 

175 

.9120 

34.4 

40.6 

5 

— 

— 

47.5 

.1850 

— 

— 

— 

45.5 

7.5 

— 

— 

51.5 

.2055 

— 

— 

— 

48.1 

10 

44.5 

.1035 

55.7 

.2270 





44.4 

51.1 

15 

— 

— 

— 

— 

165 

.9910 

— 

. 

20 

56.8 

.1475 

72 

.3095 

— 

— 

56.4 

.  — 

30 

76 

.2185 

87 

.3900 

— 

— 

70.7 



40 

101 

.3083 

101 

.4700 

— 

— 

50 

125 

.3465 

114 

.5485 

— 

— 

60 

143 

.4830 

125 

.6245 

— 

— 

70 

162 

.5690 

135 

.7030 

— 

— 

80 

179 

.6500 

145 

.9750 

— 

— 

90 

196 

.7310 

153 

.8490 

— 

— 

100 

210 

.8140 

161 

.9220 

100 

1.3750 

137 

245 

1.0850 

185 

1.1660 

— 

— 

198 

255 

1.4920 

188 

1.5340 

— 

— 

258 

218 

1.8100 

— 

— 

— 

— 

=====-— 

91 

/        OK  THK   ^J" 

MEMOIRS    ON 

The  temperature  10°  C.,  corresponding  to  the  maximum 
vapor  pressure  51  atmospheres,  appears  from  the  form  of  the 
isotherms  for  ethylene  to  be  extremely  near  the  critical  tem- 
perature. These  results  are  thus  approximately  identical 
with  the  data  obtained  by  Mr.  J.  Dewar.  The  method  pur- 
sued does  not  admit  of  a  direct  determination  of  the  point 
in  question,  and  critical  data  can  be  deduced  from  the  table 
only  by  calculation  based  on  the  intrinsic  equation  of  the 
gas. 

Quite  recently  M.  Mitkowski,*  in  an  interesting  paper  on 
the  compressibility  of  air,  has  prolonged  the  locus  of  mini- 
mum ordinates  as  far  as  145°  C.,  and  has  shown  that  this 
gas  has  a  maximum  abscissa  at  about — 75°  C.  and  124  atmos- 
pheres. 

The  form  of  the  isotherms  beyond  the  region  of  minimum 
ordinates  is  one  of  the  questions  which  I  particularly  wished  to 
investigate.  These  curves,  beginning  with  a  distance  from  the 
ordinates  in  question,  which  is  smaller  in  proportion  as  the  tem- 
perature is  lower,  seemed  to  me  to  undergo  a  transformation 
into  lines  sensibly  straight.  I  was  aware  of  the  existence  of 
slight  curvature ;  but  this  was  so  little  marked  as  to  suggest 
that  further  prolongation  of  the  family  of  curves  would  bring 
out  a  fascicle  of  parallel  straight  lines  more  and  more  clearly.  In 
fact,  this  hypothesis  proved  to  be  specially  attractive,  inasmuch 
as  the  angular  coefficient  of  these  fascicles  severally  gave  the 
limit  of  volume  for  an  infinite  pressure.  Hence  they  lead  to 
a  very  simple  interpretation  of  the  covolutne,  thus  found  direct- 
ly and  with  precision. 

Unfortunately,  this  hypothesis  of  mine  does  not  seem  to  be 
verified — at  least,  within  the  limits  of  temperature  and  pressure 
of  the  present  research.  The  isotherms  all  present  a  concavity 
towards  the  abscissa,  slight,  it  is  true,  but  nevertheless  beyond 
question.  Concavity  is  expressible  as  a  diminution  of  the  an- 
gular coefficient  of  the  tangent,  and  I  have  summarized  the 

P'  V'—PV 

values  of  the   coefficient  — - , —  —  =e  in   the   following  tn- 

f    —  mT 

ble.  This  gives  t  between  the  pressure  limits  given  in  the 
first  column  at  the  different  temperatures  indicated  in  the 
first  row. 

*  Academie  des  Sciences  de  Cracovie,  1891. 
92 


THE    LAWS    OF    GASES 


p'V' PV 

TABLE  20. — VALUES   OF  e  =      p,_p 


HYDROGEX 
€  X  106  AT 

NITROGKN 
6  X  106  AT 

AIR 
e  X  106  AT 

OXYGEN 
6  X  106  AT 

o°c. 

47.3° 

0°C. 

43.6° 

0°C. 

45.1° 

0°C. 

Aim.    Aim. 

From  500  to  1000. 
"  1000  "  1500. 
"  1500  "  2000. 
"  2000  "  2500. 
"  2500  "  8000. 

732 

690 
638 
612 
579 

693 
643 

618 

588 

1300 
1213 
1186 
1154 

1316 
1233 
1176 
1168 

1264 
1190 
1301 
1063 

1261 
1206 
1147 
1090 

1158 
1106 
1054 
1015 
971 

HYDROGKN 
t  X  106    AT 

ETHYLRXK 
e  X  106  AT 

CARBOX  DIOXIDE 

e  X  106  AT 

0°  C. 

99.  '25° 

200.5° 

o°c. 

1000° 

0°C. 

100.00 

Atm.          Aim. 

From  200  to    400 

725 
742 
730 
712 

727 
725 
725 
720 

730 
732 
719 

_ 

2357 

2180 
2080 
2002 

2195 

2157 
2090 

1715 

Ki07 
1542 
1490 

1635 
1617 
1550 

"     400  "     600  
"     600  "     800  
"     800  "  1000.. 

Clearly  the  isotherms  present  slight  curvature,  as  pointed  out 
above.  Between  the  same  pressure  limits  the  angular  coeffi- 
cient increases  by  a  small  amount  with  temperature.  This  in- 
crement corresponds  to  widening  of  the  fascicle,  which  is  dis- 
tinctly seen  for  the  case  of  carbon  dioxide  in  the  region  of 
lower  temperatures.  As  temperature  increases  the  curves  grad- 
ually cease  to  spread  apart.  In  the  permanent  gases  —  like 
hydrogen,  nitrogen,  and  air — the  variation  with  temperature  is 
scarcely  perceptible. 

A  comparison  of  the  decrements  of  these  coefficients  between 
the  same  pressure  limits  but  at  different  temperatures  shows 
no  variation  clearly  enough  indicated  to  be  specified  like  the 
preceding;  those  groups  of  observations  which  extend  over  a 
sufficient  interval  of  temperature  are  restricted  to  a  pressure 
interval  of  1000  atmospheres.  Whether  under  sufficiently  high 
pressures  and  at  high  enough  temperatures  the  angular  coeffi- 
cient will  reach  a  limiting  value  cannot,  therefore,  be  foreseen. 
In  all  cases  the  smallest  values  of  these  coefficients  are  superior 
limits  of  the  smallest  volumes  possible.  It  might  be  interest- 
ing to  compare  these  values  with  those  computed  by  aid  of  the 
intrinsic  equations.  To  take  the  simplest  form  of  equation, 
that  of  Van  der  Waals,  the  third  part  of  the  critical  volume  is 
evidently  a  limit  of  this  reduction. 


MEMOIRS    ON 

Carbon  dioxide,  for  instance,  has  a  critical  volume  of  .004224, 
the  third  of  which,  .001408,  is  markedly  less  than  the  smallest 
angular  coefficient,  .00149. 

COEFFICIENTS   OF   EXPANSION   AT   CONSTANT   PRESSURE 


/I   dv\ 

\v  dt) 


The  laws  of  expansion  are  particularly  involved  in  the  neigh- 
borhood of  the  critical  point.  For  temperatures  below  the 
critical  point  the  coefficients  can  obviously  not  be  computed 
for  pressures  intermediate  between  the  tension  maxima  corre- 
sponding to  the  given  limits  of  temperature;  for  the  change  of 
volume  here  originates  not  merely  in  thermal  expansion  between 
these  states,  but  is  due  also  to  a  change  of  state.  In  other 
words,  the  coefficients  are  infinite  between  these  limits,  and  in 
the  following  table  crosses  are  put  in  the  place  of  the  two  co- 
efficients which,  for  the  reason  given,  are  without  meaning. 

For  pressures  equal  to  the  maximum  vapor  tensions  at  one 
of  the  limits  of  the  temperature  interval,  the  coefficient  re- 
fers to  the  gaseous  state  for  the  case  of  the  lower  limit,  and 
to  the  liquid  state  for  the  case  of  the  upper  limit.  Hence,  for 
a  given  temperature  and  at  the  corresponding  maximum  vapor 
tension,  there  are  two  coefficients,  belonging,  respectively,  to 
the  two  states  of  aggregation.  One  refers  to  incipient  satura- 
tion, the  other  to  an  absence  of  vapor.  It  would  be  extremely 
interesting  to  compare  the  values  of  these  two  coefficients  at 
different  temperatures.  Such  an  inquiry,  however,  would  re- 
quire special  investigations,  and  on  the  whole  present  serious 
difficulties.  Since  the  variation  of  the  coefficient  with  tem- 
perature is  very  rapid  under  these  conditions,  it  would  be 
necessary  to  greatly  restrict  the  temperature  interval  on  ap- 
proaching saturation. 

Two  tables  follow  relative  to  carbon  dioxide  and  ethylene 
respectively,  in  which  the  mean  coefficients  of  expansion  are 
given  for  the  pressures  inserted  in  the  first  vertical  column. 
The  temperature  intervals  for  which  the  coefficients  apply  are 
shown  in  the  first  horizontal  row.  To  avoid  misapprehension, 
it  is  to  be  observed  that  the  coefficients  are  reduced  or  referred 
to  unit  of  volume  by  successively  dividing  by  the  volume  cor- 
responding to  the  lower  temperature  limit,  and  not  by  the 
initial  volume  at  zero  centigrade. 

94 





THE    LAWS    OF    GASES 


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MEMOIRS    ON 


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THE    LAWS    OF   GASES 


VARIATION    OF    THE    COEFFICIENT    OF   EXPANSION    WITH 
PRESSURE 

An  inspection  of  Table  21  shows  that  at  the  outset  the  coeffi- 
cient of  expansion  changes  with  pressure,  in  the  manner  al- 
ready specified  by  Regna-ult  for  pressures  of  a  few  atmospheres. 
It  then  passes  through  a  maximum,  which  occurs  at  a  pressure 
regularly  increasing  with  temperature.  The  maxima  in  each 
vertical  column  of  the  tables  are  put  in  parentheses.  During 
my  first  researches  on  this  subject  I  believed  that  these  maxima 
occur  at  the  same  pressure  for  which  the  product  P  V  is  a 
minimum  ;  but  the  more  extended  data  of  the  present  memoir 
show  this  law  to  be  only  approximate. 

At  the  critical  temperature  the  maximum  coefficient  of  ex- 
pansion evidently  coincides  with  the  critical  pressure,  since  the 
former  is  then  infinite.  Under  other  conditions,  depending  on 
the  form  of  the  isotherm,  this  pressure  is  much  smaller  than 
the  pressure  corresponding  to  the  minimum  ordinate.  The 
locus  of  maximum  coefficients  of  expansion  thus  starts  out  from 
the  critical  point  (in  my  first  memoir  the  initial  isotherm  was 
taken  at  35.1°  C.);  and  since  this  is  a  point  of  double  inflection, 
the  inquiry  is  pertinent  whether  the  locus  in  question  is  not 
identical  with  the  point  of  inflection  of  the  isotherms.  This  is 
not  the  case.  For  increasing  temperature,  the  maximum  co- 
efficient is  always  encountered  a  little  earlier  than  the  mini- 
mum ordinate.  It  is  thus  comprehended  between  the  locus  of 
the  summits  of  these  ordinates  and  the  locus  of  the  points  of 
inflection.  Little  by  little  it  approaches  the  former,  and  ends 
by  intersecting  it  in  the  region  of  its  minimum  abscissa. 

Table  22  for  ethylene  leads  to  a  series  of  results  of  an  analo- 
gous character  throughout. 

The  following  table  (23)  shows  for  oxygen,  hydrogen,  nitro- 
gen, and  air  that  the  diminution  of  the  coefficient  of  expansion 
continues  regularly  even  as  far  as  3000  atmospheres.  The  same 
fact  is  exhibited  in  Table  24  for  the  same  gases  throughout 
higher  temperatures. 


MEMOIRS    ON 


1     Ay 
TABLE    23. — VALUES    OF    - 


p 

OXYGEN 

HYDROGEN 

^mospheres 

0°—  15.6° 

00—15.40 

90—47.30 

1000 

.00236 

.00200 

.00206 

1500 

189 

178 

173 

2000 

164 

152 

152 

2500 

147 

138 

137 

3000 

134 

128 

129 

P 

NITROGEN 

AlR 

Atmospheres 

0°—  16.0° 

Oc_46.6° 

00—15.70 

00—45.10 

1000 

.00193 

.00191 

.00206 

.00197 

1500 

140 

151 

144 

148 

2000 

133 

131 

116 

126 

2500 

111 

108 

107 

112 

3000 

098 

098 

110 

105 

VARIATION    OF   THE    COEFFICIENT  OF   EXPANSION    WITH 
TEMPERATURE 

The  above  tables,  21  and  22,  show  that  the  coefficient  at  first 
increases  with  temperature,  passes  a  maximum,  and  thereafter 
diminishes. 

Under  constant  pressures  of  successively  increasing  value  the 
maximum  occurs  at  temperatures  which  continually  increase, 
while  the  maximum  itself  becomes  less  accentuated  and  finally 
vanishes  within  the  limits  of  the  tables.  An  increase  of  value 
alone  remains,  which,  in  its  turn,  gradually  becomes  less  ap- 
preciable. At  1000  atmospheres  the  maximum  is  certainly  still 
encountered  at  sufficiently  high  temperatures.  To  verify  these 
observations  it  suffices  to  treat  such  gases  as  are  much  farther 
removed  from  their  critical  points.  It  is  then  manifest  that 
the  maximum  has  been  reached  or  even  passed  in  all  cases,  as, 
for  instance,  Table  24  fully  evidences.  All  the  coefficients  are 
here  notably  smaller  between  100°  and  200°  than  between  0° 
and  100°.  Henee  the, maximum  has  been  passed. 


THE    LAWS    OF    GASES 


1    A® 
TABLE    24. — VALUES    OF  -       -  =  a 

V   At 


OXYGEN 

HYDROGEN 

NITROGEN 

AIR 

0°  to 

99.50  to 

0°  to 

99.25°  to 

0°to 

99.45°  to 

0°  to 

99.4°  to 

99.5° 

199.5° 

99.  25<> 

209.2° 

99.45° 

199.50° 

99.4° 

200.4° 

Aim. 

a 

0 

a 

a 

a 

a 

a 

a 

100 

,00486 

— 









.00444 



200 

534 

.00300 

.00332 

.00242 

.00433 

.00280 

455 

.00287 

800 

512 

297 

314 

231 

402 

267 

422 

275 

400 

459 

280 

295 

221 

358 

250 

371 

261 

500 

405 

264 

278 

214 

315 

235 

331 

241 

600 

357 

245 

261 

204 

282 

219 

294 

222 

700 

320 

226 

249 

196 

256 

204 

269 

207 

800 

288 

212 

237 

189 

236 

189 

244 

194 

900 

261 

198 

226 

182 

218 

179 

226 

182 

1000 

241 

— 

218 

-- 

— 

— 

214 

171 

In  Tables  21  and  22  the  maxima  relative  to  temperature  were 
put  in  square  brackets.  It  is  seen  that  they  make  up  a  group 
which  lies  very  close  to  the  maxima  relative  to  pressure,  and 
which,  like  the  latter,  would  appear  with  greater  regularity  if 
the  limits  of  the  temperature  and  the  pressure  intervals  were 
both  narrower.  The  real  maxima  coincide,  as  it  were,  acci- 
dentally with  the  numbers  in  the  tables. 

The  locus  of  the  maxima  relative  to  temperature  starts  from 
the  critical  point,  as  did  the  locus  of  the  maxima  relative  to 
pressure.  It  approaches  the  locus  of  minimum  ordinates  more 
rapidly  than  the  latter,  and  intersects  it  sooner,  as  it  were. 

Below  the  critical  temperature  the  first  coefficients  of  each 
horizontal  row  in  Table  21  refer  to  the  liquid  state,  since  the 
pressure  exceeds  the  maximum  vapor  tension.  At  pressures 
lower  than  the  critical  pressure  the  coefficients  for  the  gaseous 
state,  properly  so  called,  at  once  decrease.  As  early  as  1870  I 
showed  *  that  for  the  cases  of  carbon  dioxide  and  sulphur  di- 
oxide the  coefficients  decrease  regularly  from  0°  C.  to  above 
300°  under  atmospheric  pressure. 

For  pressures  of  a  value  higher  than  the  critical  pressure 
there  is  no  further  occasion  to  consider  the  distinction  between 
the  two  coefficients  which  I  have  just  explained ;  for  the  dis- 
continuity no  longer  occurs  under  constant  pressure.  To  ob- 
viate all  misapprehension  I  have  marked  three  coefficients  with 
an  asterisk  (*),  which,  although  corresponding  to  temperatures 

*  Comptes  Rendus,  July  4, 1870;  Annales  de  CUimie  et  de  Physique,  1872. 

99 


MEMOIRS    ON 

below  the  critical  temperature,  belong  to  the  gaseous  state  (at 
50  and  60  atmospheres). 

To  return  to  the  gaseous  state  :  It  was  shown  above  that  in 
case  of  oxygen,  hydrogen,  nitrogen,  and  air  the  coefficient  of 
expansion  has  passed  beyond  its  maximum  value  even  at  ordi- 
nary temperatures.  The  following  table  (25*),  containing  values 

_\  f) 

of  —  -  not  reduced  to  the  unit  of  volume,  proves  that  the  coeffi- 

cients are  practically  independent  of  temperature,  oxygen  alone 
excepted  : 


TABLE  25*.  —  VALUES  OF  -  xlO8 

A  t 


p 

OXYGEN 

HYDROGEN 

NITROGEN 

AIR 

0°  to 
9950 

99.5°  to 
199.5° 

0°to 
99.25° 

99.25°  to 
200.2° 

0°to 

99.5° 

99.45°  to 
199.5° 

0°to 

99.4° 

99.  4°  to 
200° 

Atm. 

100 

4518 



— 

— 



— 

4320 



200 

2442 

2095 

1890 

1835 

2251 

2086 

2296 

2095 

300 

1643 

1440 

1265 

1222 

1522 

1414 

1544 

1422 

400 

1207 

1072 

947 

919 

1124 

1066 

1125 

1084 

500 

937 

856 

754 

741 

877 

859 

887 

859 

600 

756 

703 

624 

615 

718 

715 

720 

706 

700 

634 

592 

535 

526 

609 

609 

615 

602 

800 

541 

512 

468 

460 

530 

525 

533 

525 

900 

470 

450 

415 

409 

469 

463 

469 

463 

1000 

418 

— 

376 

— 

— 

— 

425 

413 

Thus  the  coefficients  beginning  with  0°C.  are  sensibly  constant 
for  a  given  pressure,  the  same  fact  which  was  brought  out  by 
Table  23  as  far  as  the  highest  pressures.  Hence  the  coefficients 
computed  for  the  successive  intervals  vary  nearly  inversely  as 
the  successive  initial  volumes.  This  appears  to  be  the  law  tow- 
ards which  the  decreasing  march  which  follows  the  maximum 
points  converges  for  conditions  of  increasing  temperature.  This 
limiting  state  is  reached  sooner  in  proportion  as  the  pressure  is 
smaller. 

Hence,  at  all  pressures  and  sufficiently  high  temperatures, 
this  simple  law  supervenes  :  the  increment  of  volume  is  pro- 
portional to  increment  of  temperature  reproducing  the  case  of 
perfect  gases.  In  a  general  way  only  is  the  volume  proportional 
to  the  absolute  temperature  increased  by  a  constant ;  for  this 
constant  diminishes  as  pressure  decreases  in  such  a  way  that  if 
pressure  is  small  enough,  the  law  of  the  proportionality  of  vol- 

100 


THE    LAWS    OF    GASES 

ume  and  absolute  temperature  is  encountered.     This  again  is 
the  law  of  sensibly  perfect  gases. 

COEFFICIENTS    OF    EXPANSION    AT    CONSTANT    VOLUME, 

1  dp  dp 

3— 7^,  AND  PRESSURE  COEFFICIENTS.  B  =  -^- 

p  dt  dt 

To  avoid  all  confusion,  I  will  call  the  values  — j  pressure  co- 
efficients. This  reserves  for  -  ~  the  time-honored,  but  other- 
wise very  curious  designation  of  expansion  coefficient  at  con- 
stant volume. 

In  Table  25,  on  page  102,  computed  by  aid  of  the  data  in 
Tables  6,  12,  17,  18,  these  coefficients  are  given  relative  to 
the  temperature  interval  inserted  at  the  heads  of  the  vertical 
columns,  and  for  the  constant  volume  in  the  first  of  these 
columns.  The  pressures  indicated  for  carbon  dioxide  and 
ethylene  under  the  caption  "Initial  Pressures"  do  not  all  refer 
to  zero,  but  to  the  lower  limit  of  temperature  of  the  first  mean 
coefficient  on  the  same  horizontal  row.  The  tables  contain  a 
gap  which  corresponds  to  the  region  contained  within  the  curve 
of  liquefaction. 

It  must  be  borne  in  mind  that  reduction  to  the  unit  of  press- 
ure of  the  coefficients  /3  has  been  accomplished  by  dividing  by 
the  pressure  corresponding  to  the  lower  temperature  of  each 
interval  —  at  variance,  therefore,  to  the  notation  frequently 
adopted.  I  have  already  made  a  similar  remark  relative  to  the 
reduction  of  the  coefficients  of  compressibility  and  of  expansion 
under  constant  pressure  to  the  unit  of  volume. 


MEMOIRS    ON 


CQ. 

ft          ° 

5 


t>  OO  t—  O5  00  O  i> 

to  10  «>  os  co  oo  co 

CO  CO  CO  CO  CO  CO  Tj< 


»c  o  co  oo  oo  y, 
t-  to  co  io  ic  a 

r-H  CO   CO  ^f  tO  O 


COO500COi>COCOODT-i 


8  os  01  10  t— 
r-coco  co 

T-I  CO  CO  JO  J> 


i  i 


t£oot>S  co  c^Jo  co^    I     I 

t— iCOCOJOi>OCDOOi>     I      I 
T- i  T— i  CO  rf 


OSCOCOCOCO^COt-' 
T-H£>OJOCOZ>T-iO' 


OS  O  OS  JO  3D  CO  "*  J>  t-  »>•     I 

T-iCOCOJOi>T-iJ>O500CO     I 
1-1  TH  CO  Tf  OO 


5O  CD  -* 
-i-i  t>  O  Oi 
OS  CO 


»O  O  O  O  O 
OSlOt>COGQ 


PS 

iis 


J>  CO  QO  JO  {> 
00  O  t-  Tfi  1O 
^  CO  CO  00  O 


-r-i  OS  <M 
00  T-H  JO 
Q0500 


OO1OOOJO 
O5r-iOOO'-iJO 


JOO1OJO 


CO  00  1-1  CO 


IN  i  i  i 


»^COOOOOOOCOOOOt- 

00  TO  <O  O1  CO  t>»  C^t  f- •*  4O  O5  OO 

COr^T^S^10^50^051" 

102 


CO  T— i  JO  C~  T-H  T— i  CO  I   I 

CO  CO  00  JO  T-<  10  CO  I   I 


I' 


•^  •<*  CO  i>  00  i 


1 1>  TH  co  T-I  as  1-1  o 

•  «>  — i  ^  ao  os  1-1  co 

JO  i>  00  OS  O  I-H  O5 


TH  rH  C     CO  Tt*  1O     2 


JO  O  JO  O  JO  O  CO 
CO  CO  *>  -00  CO  1-1  CO 


00     i      i      i      i      1    T-HO  JO 

CO  t-  rH  CO 

00     '      '      !  '    O  00  O^ 


10 

OO 


COOCOOOOCOOOC- 


CO  —  00  CO  JO  rt<  CO  CO  O7 


THE    LAWS    OF    GASES 


TABLE  26. — VALUES   OF   B  AND   & 


PRESS- 

HYDROGEN 

OXYGEN 

UK  KS 

CONSTANT 

CONSTANT 

AT 
ZKRO. 

VOLUMES 

0°—  99.  '2° 

99.2°-  200.  5° 

VOLUMES 

0°—  99.5° 

99.50—199.50 

ATM. 

FX10« 

5xio3 

/3X105 

5X103 

/3X106 

rxio" 

5X103 

/3X105 

5X103 

/3X105 

100 

10690 

373 

373 

366 

267 

9265 

492 

492 

470 

315 

200 

5690 

766 

383 

742 

269 

4570 

1226 

613 

1115 

357 

300 

4030 

1149 

383 

1129 

272 

3208 

2090 

696 

1900 

374 

400 

3207 

1521 

380 

1475 

268 

2629 

2924 

731 

2570 

372 

500 

2713 

1895 

379 

1842 

267 

2312 

3698 

740 

— 

— 

600 

2386 

2256 

376 















700 

2149 

3710 

371 

— 

— 

— 

— 

— 

— 

— 

PRESS- 

NITROGEN 

AIR 

URES 

CONSTANT 

CONSTANT 

AT 
ZERO. 

VOLUMES 

0°—  99.4° 

99.40—199.60 

VOLUMES 

00—99.40 

99.40—200.4° 

ATM. 

FX106 

5X103 

,3X10* 

5X103 

/3X105 

FXIO* 

5X103 

/3X1Q5 

5X103 

/3X105 

100 

9910 

462 

462 

460 

315 

9730 

462 

462 

465 

319 

200 

5195 

1075 

537 

1070 

349 

5050 

1105 

552 

1090 

351 

300 

3786 

1748 

582 

1700 

359 

3658 

1800 

600 

1742 

364 

400 

3142 

2382 

595 

2320 

364 

3036 

2470 

617 

2327 

360 

500 

2780 

2982 

596 

— 

— 

2680 

3085 

617 



— 

600 

2543 

3582 

597 

— 

— 

2450 

3718 

620 

— 

— 

TABLE  27. — VALUES   OF   B  AND   /3 


PRESS- 

HYDROGEN 

OXYGEN 

URES 

CONSTANT 

CONSTANT 

AT 
ZERO. 

VOLUMES 

.60—15.40 

00—47.30 

VOLUMES 

0°—15.60 

ATM. 

FX10« 

5x103 

/3X105 

5X103 

/3X1Q5 

FX106 

5X103 

/3X10 

600 











2117.0 



4423 

737 

800 





— 

— 

— 

1880.0 



5641 

705 

1000 

1725.0 

3571 

357 

3467 

347 

1736.0 



6795 

679 

1200 

1557.5 

4155 

346 

4017 

335 

1635.0 



8013 

668 

1500 

13800 

5129 

342 

5010 

334 

1497.5 

(1600  atm) 

10513 

657 

1800 

1258.0 

5779 

321 

5729 

318 

— 

— 



— 

2000 

1194.5 

6428 

321 

6342 

317 

1408.0 

— 

12051 

602 

2400 

1097.5 

7662 

319 

7315 

305 

1343.5 

— 

13974 

580 

2800 

10245 

8117 

325 

— 

— 

1304.0 

(2700  atm.) 

14423 

538 

PRESS- 

NITROGEN 

AIR 

URES 

CONSTANT 

CONSTANT 

AT 
ZKKO. 

VOLUMES 

00—16.0° 

00-43.60 

VOLUMES 

00—15.70 

00-45.1° 

ATM. 

FX10" 

5X103 

/3X105 

5X103 

/3X105 

FX10« 

5X103 

,3X105 

5X103 

/3X10- 

800 







. 



2171.0 

4841 

605 

4591 

574 

1000 

2070.0 

5500 

550 

5481 

548 

1999.0 

5668 

567 

5543 

554 

1200 

1946.0 

6125 

510 

6284 

524 

1883.0 

6051 

504 

6075 

506 

1500 

1813.5 

7060 

471 

7155 

477 

1754.0 

7006 

467 

7273 

485 

1800 

1714.5 

8562 

475 

8440 

469 

1662.0 

7900 

439 

8115 

451 

2000 

1663.5 

9375 

468 

9197 

460 

1613.0 

8344 

417 

8736 

437 

2400 

1583.5 

10750 

448 

10505 

437 

1533.5 

9681 

403 

9888 

412 

2800 

1525.0 

11875 

424 

— 

— 

— 

— 

— 

— 

— 

103 


MEMOIRS    ON 


VARIATION    OF   THE    COEFFICIENTS   B  AND   /3   WITH   VOLUME 

The  pressure  coefficient  B  is  seen  to  increase  very  rapidly 
when  volume  decreases — i.e.,  when  the  initial  pressure  at  zero 
increases.  The  coefficient  ft  (Table  25)  at  first  increases  for  in- 
creasing volume,  and  thereafter  passes  through  a  maximum 
which  is  much  less  pronounced  when  the  temperature  is  higher. 
Finally  ft  decreases  with  increasing  volume.  In  case  of  nitro- 
gen the  maximum  is  not  yet  reached  between  0°  and  200° 
within  the  pressure  limits  given  in  Table  26.  For  hydrogen,  on 
the  contrary,  its  occurrence  falls  within  the -same  limits,  since 
ft  is  then  sensibly  constant.  For  the  highest  pressures  the 
maximum  has  been  passed  by  in  case  of  each  of  the  four  gases 
in  Table  27. 

VARIATION    OF   THE    COEFFICIENTS   £  AND   /3    WITH   TEM- 
PERATURE 

Generally  speaking,  the  coefficient  B  varies  very  little  with 
temperature.  An  inspection  of  the  table  shows  for  carbon 
dioxide  between  0°  and  100°  that  this  variation  is  quite  in- 
significant. This  is  the  identical  result  reached  in  my  re- 
search* of  1881.  Some  time  after  Messrs.  W.  Ramsay  and 
Sidney  Young  published  important  researches  on  the  same  sub- 
ject, to  which  I  shall  recur  on  another  occasion. 

Between  100°  and  260°,  B  shows  a  slight  diminution.  This 
is  also  true  for  the  case  of  ethylene. 

For  hydrogen,  air,  and  nitrogen  the  variation  of  B  between 
0°  and  200°  (Table  26)  is  scarcely  apparent,  particularly  after 
the  pressures  approach  the  high  values.  A  similar  influence 
may  be  drawn  for  the  other  three  gases  (Table  27)  for  a  press- 
ure interval  quite  up  to  the  highest  pressures.  It  must  be  ob- 
served, however,  that  these  results  are  restricted  to  smaller 
temperature  intervals. 

It  appears  to  follow  from  the  results  as  a  whole  that  the 
variation  of  the  pressure  coefficient  with  temperature,  always 
very  small,  quite  vanishes  at  sufficiently  high  temperatures  and 
probably  at  all  temperatures  under  sufficiently  high  pressures. 
This  is  evidenced  by  the  results  shown  by  those  gases  which, 
within  the  temperature  limits  of  the  present  research,  are  al- 

*  Annales  de  Chimie  et  de  Physique,  5e  Serie,  vol.  xxii. 
104 


THE    LAWS    OF    GASES 

ready  in  a  thermal  state  far  above  their  critical  points.  Under 
these  conditions  the  pressures  corresponding  to  constancy  of 
volume  are  not  proportional  to  the  respective  absolute  tem- 
peratures ;  they  are  proportional  to  them  when  each  is  dimin- 
ished by  a  constant  function  of  volume  only.  This  constant  is 
numerically  a  number  of  degrees,  and  it  at  first  increases  rap- 
idly when  volume  diminishes  ;  thereafter  it  passes  through  a 
maximum,  decreases  passing  through  zero  into  negative  values, 
and  continues  to  decrease  in  absolute  value.  Whenever  this 
constant  vanishes  the  gas  is  clearly  characterized  by  the  law  of 
perfect  gases,  and  this  happens  in  the  case  of  hydrogen  at 
about  800  atmospheres.  It  is  exceedingly  remarkable  that 
under  these  special  conditions  the  value  of  the  pressure  co- 
efficient is  nearly  equal  to  the  value  which  holds  for  normal 
pressure — i.e.,  to  that  attributed  to  gases  when  they  approach 
as  nearly  as  possible  to  the  state  of  a  perfect  gas.  It  would  be 
extremely  interesting  to  discover  whether  the  observation  in 
question  is  of  general  significance.  Unfortunately,  the  other 
gases  studied  have  not  under  the  highest  pressures  applied 
reached  the  state  for  which  the  constant  in  question  vanishes. 

The  variations  of  the  constant  ft  may  be  deduced  from  what 
has  just  been  stated.  In  every  case  this  coefficient  for  a  given 
volume  varies  very  nearly  inversely  to  pressure.  In  the  region 
comprised  within  the  curve  of  liquefaction,  and  corresponding 
to  the  gap  in  Table  25  (carbon  dioxide),  there  is  no  true  pressure 

coefficient.     The  values   -£  now  refer  to  the  maximum  vapor 

tl  t 

tensions  and  no  longer  vary  with  volume.  Necessarily  an 
abrupt  variation  of  these  values  occurs  on  breaking  across  the 
curve  of  liquefaction,  excepting,  perhaps,  the  line  of  equal  vol- 
umes, which  passes  through  the  critical  point  with  an  inver- 
sion of  the  sign  of  the  variation  on  one  side  or  the  other  of  this 

line.     Indeed,  it  is  easily  observed  that  the  values  of  yr  for  the 

lines  of  equal  volume  passing  above  the  critical  point  and  near 
the  curve  of  saturation  are  smaller  on  the  outside  than  on  the 
inside  of  this  curve.  The  contrary  will  be  the  case  for  the 
lines  of  equal  volume  which  pass  below  the  critical  point.  In 
every  case  the  above  inferences  relative  to  pressure  coefficients 
seem  to  be  immediately  applicable  as  soon  as  the  curve  of 
liquefaction  is  left  behind. 

105 


MEMOIRS    ON 

The  isotherms  below  the  critical  point  are  difficult  to  map 
out  in  those  parts  which  are  contiguous  with  the  curve  of 
liquefaction.  This  curve  cannot  be  obtained  by  means  of  the 
above  experiments  as  accurately  as  may  be  done  by  comparing 
the  densities  of  the  liquid  and  of  the  vapor  obtained  in  experi- 
ments specially  designed  for  this  purpose.  I  have  carried  out 
measurements  of  this  kind  for  carbon  dioxide  between  zero  and 
the  critical  point;  but  I  will  not  enter  into  details  relative  to 
these  results,*  as  they  lie  outside  of  the  scope  of  the  present  in- 
vestigation, beyond  giving  a  tabulated  view  of  the  data.  The 
agreement  between  the  present  values  of  maximum  vapor  tension 
and  those  contained  in  the  above  tables  is  apparent.  The  same 
research  furnished  the  following  elements  of  the  critical  point : 

Critical  temperature 31.35° 

Critical  pressure 72.9     aim. 

Critical  density 0.464 

TABLE  28. — DATA    FOR   CARBON    DIOXIDE 


DENSITY    OP  THE 

DENSITY   OP    THE 

MAXIMUM 

MAXIMUM 

T 

LIQUID 

VAPOR 

VAPOR 
TENSION 

T 

LIQUID 

VAPOR 

VAPOR 
TENSION 

Deg. 

Aim. 

Deg. 

Atm. 

0 

.914 

.096 

34.3 

18 

.786 

.176 

53.8 

1 

.910 

.099 

35.2 

19 

.776 

.183 

55.0 

2 

.906 

.103 

36.1 

20 

.766 

.190 

56.3 

3 

.900 

.106 

37.0 

21 

.755 

.199 

57.6 

4 

.894 

.110 

38.0 

22 

.743 

.208 

59.0 

5 

.888 

.114 

39.0 

23 

.731 

.217 

60.4 

6 

.882 

.117 

40.0 

24 

.717 

.228 

61.8 

7 

.876 

.121 

41.0 

25 

.703 

.240 

63.3 

8 

.869 

.125 

42.0 

26 

.688 

.252 

647 

9 

.863 

.129 

43.1 

27 

.671 

.266 

66.2 

10 

.856 

.133 

44.2 

28 

.653 

.282 

67.7 

11 

.848 

.137 

45.3 

29 

.630 

.303 

69.2 

12 

.841 

.142 

46.4 

30 

.598 

.334 

70.7 

13 

.831 

.147 

47.5 

30.5 

.574 

.356 

71.5 

14 

.822 

.152 

48.7 

31.0 

.536 

.392 

72.3 

15 

.814 

.158 

50.0 

31.25 

.497 

.422 

72.8 

16 

.806 

.164 

51.2 

31.35 

.464 

.464 

72.9 

17 

.796 

.170 

52.4 

*  Gomptes  Rendus,  May  16,  1892  ;  June  7, 1892. 
1892;  Seances  de  la  Soc.  de  Physique,  1892. 

106 


Cf.  Journal  de  Physique, 


THE    LAWS    OF    GASES 

I  have  not  up  to  the  present  time  been  able  to  repeat  the 
same  work  for  ethylene. 

Certain  other  properties  of  the  isotherms  for  carbon  dioxide 
and  ethylene,  as  well  as  divers  inquiries  of  a  more  theoretical 
kind,  are  not  in  place  here.  In  the  present  memoir,  as  well 
as  in  the  following  work  relating  to  liquids,  I  have  purposed 
merely  to  exhibit  the  experimental  methods,  to 'publish  the 
numerical  results  obtained,  and  to  deduce  from  them  such  gen- 
eral laws  as  result  from  inspection. 

EMILE  HILAIRE  AMAGAT  was  born  on  the  2d  of  January, 
1841,  at  St.  Satur,  a  village  in  the  arrondissement  de  Sancerre, 
in  the  Departement  du  Cher.  It  was  at  first  his  intention  to  be 
a  technical  chemist,  but  he  abandoned  this  career  almost  at  the 
very  outset  in  preference  of  one  in  pure  science. 

For  several  years  Amagat  was  preparateur  of  the  celebrated 
Berthelot  at  the  College  de,  France.  After  this  (between  1867 
and  1872)  he  was  called  to  Switzerland,  where  he  served  as  pro- 
fessor at  the  Lycee  de  Fribourg.  It  was  there  that  Amagat  com- 
pleted his  these  de  doctoral,  being  formally  honored  with  this 
degree  in  Paris  in  1872. 

Returning  to  France,  he  was  successively  made  professor  at 
the  Lycee  d'Alencon,  a  I'Ecole  Normale  Specialede  Cluny,  and  in 
1877  was  appointed  professor  of  physics  in  i\\e  Faculte  Libre  des 
Sciences  of  Lyons.  In  this  institution,  then  merging  into  active 
existence,  he  created  the  department  of  physics,  and  in  it  con- 
ducted his  most  famous  researches. 

He  left  Lyons  in  1891  for  Paris,  where  he  resides  at  present 
in  the  official  position  of  examinateur  a  I'Ecole  Poly  technique. 

Amagat  has  been  correspondent  of  the  Institut  de  France 
(Academic  des  Sciences,  Section  de  Physique)  since  1889.  He 
was  elected  a  foreign  member  of  the  Royal  Society  of  London 
in  1897,  and  of  the  Royal  Society  of  Edinburgh  in  the  same  year. 
He  is  honorary  member  of  the  Societe  Hollandaise  des  Sciences, 
of  the  Societe  Scientifique  de  Bruxelles,  of  the  Philosophical 
Society  of  Manchester,  etc.,  etc. 


BIBLIOGRAPHY 

AMONG  Amagnt's  papers  those  bearing  particularly  on  the  laws  of  gases 
may  be  summarized  for  the  reader's  convenience  as  follows.  A  complete 
list  of  Amagat's  researches  will  be  found  in  a  pamphlet  published  by 
Gautier-Villars  et  tils,  Paris,  1896,  entitled:  Notice  sur  les  Travaux  Scien- 
(ifiques  de  M.  E.  H.  Amac/at. 

De  {'influence  de  la  temperature  sur  les  ecartes  de  la  loi  de  Mariotte  ;  C.  JR., 

Ixviii.,  p.  1170,  1869. 

Sur  la  compressibilite  du  gaz  ;  C.  R.,  Ixxi.,  p.  67,  1870. 
Sur  la  dilatation  et  la  compress,  des  gaz  ;  C.  R.,  Ixxiii.,  p.  183,  1871. 
Sur  la  compress,  de  1'hydrogene  et  de  1'air  a  des  temperatures  elevees ; 

C.  R.,  Ixxv.,  p.  479,  1872. 

Sur  la  dilatation  des  gaz  humides;  C.  R.,  Ixxiv.,  p.  1299,  1872. 
Compress,  de  1'air  et  de  1'hydrogene  a"  des  temperatures  elevees  ;  Annales 

de  Chimie  et  de  Physique  (4),  xxviii.,  1873. 
Dilat.  et  compress,  des  £nz  a  divers  temperatures  ;  Annales  de  Chimie  et  de 

Physique  (4),  xxix.,  1873. 
Recherches  sur  1'elasticite  de  1'air  sur  de  faibles  pressions  ;  G.  R.,  Ixxxii., 

p.  914,  1876  ;  ibid.,  Annales  de  Chimie  et  de  Physique  (5),  viii.,  1876. 
Sur  la  compress  des  gaz  a  depressions  elevees  ;  C.  R.,  Ixxxvii.,  p.  432, 

1878.     (Preliminary  work  at  Fort  Saint-Just.) 
Experiences  du  puits  Verpilleux  ;  C.  R.,  Ixxxviii.,  p.  336,  1879. 
Sur  la  compress,  des  divers  gaz  a  des  pressions  elevees;  C.  R.,  Ixxxix., 

p.  439,  18^9. 

Influence  de  la  temperature  sur  la  compress,  des  gaz  sous  de  fortes  pres- 
sions; C.  R.,  xc.,  p.  994,  1880. 
Sur  la  dilatation  et  la  compress,  des  gaz  sous  de  fortes  pressions  ;  C.  R., 

xci.,  p.  428,  1880. 
Sur  la  compress,  de  I'oxyire'm',  et   1'action  de  ce  gaz  sur  le  mercure,  etc.; 

C.  R.,  xci.,  p.  812,  1880. 
Sur  la  compress,  de  1'acide  carboniqtie  et  de  1'air  sous  t'aible  pression  et 

temp,  elevee  ;  G.  R.,  xciii.,  p.  306,  1881. 
Memoire  sur  la  compressibilite  des  g?iz  aux  fortes  pressions  ;  Annales  de 

Chimie  et  de  Physique  (5),  xxii.,  1881. 
Sur  la  relation  0  (p,  v,  t')=0  relative  aux  gaz,  etc. ;  C.  R.,  xciv.,  p.  847, 

1882. 

Sur  1'elasticite  des  gaz  rarefies  ;   C.  R.,  xcv.,  p.  281,  1882. 
Sur  ....  la  compress,  du  gaz  azote  ;   C.  R.,  xcv.,  p.  638,  1882. 

108 


MEMOIRS    ON    THE    LAWS    OF    GASES 

Sujets  relatifs  a  1'etude  du  gaz  ;  Annales  CMmie  et  de  Physique  (5),  xxviii., 

1883. 
Memoire  sur  la  compress,  de  Pair  et  de  1'acide  carbonique  .  .  ;  Annales  de 

CMmie  et  de  Physique  (5),  xxviii.,  1883. 
Memoire  sur  la  compress,  de  Fair,  de  1'hydrogene  et  de  1'acide  carbonique 

rarefies  ;  Annales  de  Chimie  et  de  Physique  (5),  xxviii.,  1883. 
Sur  une  forme  nouvelle  de  la  fonction  0  (p,  v,  t)=Q  ;  Annales  de  Chimie 

et  de  Physique  (5),  xxviii.,  1883. 
Resultats  pour  servir  aux  calculs  des  manometres  a  gaz  ;  C.  R.,  xcix., 

p.  1017,  1884. 

Note  relative  a  une  erreur  .  .  .  .  ;  C.  R.,  xcix.,  p.  1153,  1884. 
Sur  la  densite  liraite  et  de  volume  atomique  des  gaz,  etc.;  C.  R.,  c.,  p.  633, 

1885. 

Sur  la  volume  atomique  de  1'oxygSne ;  C.  It.,  cii.,  p.  1100,  1886. 
Compressibilite  des  gaz  :  oxygene,  hydrogene,  azote  et  air  jusqu'a  3000 

atm.;  C.  R.,  cvii.,  p.  522,  1888. 
Nouvelle  methode  pour  1'etude  de  la  compress,  et  de  la  dilatation  des 

liquides  et  des  gaz  .  .  .  .  ;  C.  R.,  cxi.,  p.  871,  1890. 
Sur  la  determination  de  la  densite  des  gaz  etde  leurvapenr  snturee  .  .  .  .  ; 

C.  R.,  cxiv.,  p.  1093, 1892  ;  ibid.,  C.  R.,  cxiv.,  p.  1322, 1892  ;  Journal 

de  Physique,  p.  288,  1892. 
Sur  les  lois  de  dilatations  des  gaz  sous  pression  constante ;  C.  R.,  cxv., 

p.  771,  1892. 
Sur  la  comparaison  des  lois  de  dilatation  des  liquides  et  de  celles  des 

gaz,  etc.;  C.  R.,  cxv.,  p.  919,  1892. 
Sur  les  lois  de  dilatation  a  volume  constant  des  fluides  .  .  .  .  ;  C.  R.,  cxv., 

p.  1041,  1892. 
Memoires  sur  1'elastioite  et  la  dilatation  des  fluides  jusqu'aux  tre"s  hautes 

pressions  ;  Annales  de  Chimie  et  de  Physique  (6),  xxix.,  1893. 
Sur  la  pression  interieure  dans  le  gaz  ;  C.  R.,  cxviii.,  p.  326,  1894 ;  ibid., 

C.  R.,  cxviii.,  566,  1894. 

Sur  la  pression  interieure  et  le  viriel  .  .  .  .  ;  C.  R.,  cxx.,  p.  489,  1895. 
Verification  d'ensemble  de  la  loi  des  etats  correspondants  de  Van  der  Waals; 

C.  R.,  cxxiii.,  p.  30,  1896  ;  ibid.,  C.  R.,  cxxiii.,  p.  83,  1896. 

The  titles  of  a  few  relevant  papers  by  other  investigators  follow: 

RELATIONS  BETWEEN  PRESSURE,  VOLUME,  AND  TEMPERATURE 

Ramsay  and  Young,  Philosophical  Transactions,  177,  178,  18O,  183. 

Barus,  C.,  Philosophical  Magazine  (5)  3O,  338-361,  1890.- 

Tait,  P.  G.,  "Challenger   Reports,"  Physics  and  Chemistry,  vol.  ii., 

part  iv. ;  Proceedings  of  tlie  Royal  Society  of  Edinburgh, 
vols.  xii. ,  xiii.,  xx. 
Leduc,  A.,  Journal  de  Physique  (3),  7,  1898. 

Annales  de  Chimie  et  de  Physique,  15,  5-115,  1898. 
Wroblewski,         Wiedemann,  Annalen,  29,  428,  1886. 
Rose-Innes,  Philosophical  Magazine,  44,  45,  1897,  1898. 

109 


MEMOIRS    ON    THE    LAWS    OF   GASES 

CONTINUITY  OF  LIQUID  AND  GASEOUS  STATES 

Van  dor  Waals,  "On  the  Continuity  of  the  Liquid  and  Gaseous  States." 
Translation.  London,  1890.  (Original  Dutch  edition, 
1873.) 

Clausius,  R.,        Wiedemann,  Annalen,  9,  337,  1880. 

Sarrau,  Comptes  Rendus,  1 1O,  880,  1890. 

Ramsay  and  Young,  Philosophical  Magazine  (5),  23,  24,  1887. 

Brillouin,  M.,       Journal  de  Physique  (3),  2,  113,  1893. 

Tait,  P.  G.,  Transactions  of  the  Royal  Society  of  Edinburgh,  36,  1891. 

Nature,  44,  45, 1891. 

Rayleigh,  Lord,  Nature,  44,  45,  1891. 

Bakker,  G.,  Zeitschrift  filr  Physikalische  Chemie,  21,  127,  1896. 

Young,  S.,  Philosophical  Magazine  (5),  33,  153,  1892  (37,  1,  1894). 

CRITICAL  STATE 

Andrews,  Philosophical  Transactions,  166,  421-449,  1876. 

Cailletet  and  Colardeau,  Annales  de  Chimie  etdePhyxique(§},  25,  519,  1892. 
Mathias,  E.,         Journal  de  Physique  (3).  1.  53,  1892. 
Kuenen,  J.  P.,     Philosophical  Magazine,  44,  1897. 


THE  END. 


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